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According to numerous surveys and reviews from people related to IT, the book which they recommend to start your journey as an IT specialist is The Code: Secret Language of Computer Science by Charles Petzold.
Comprehensive IT basics explained through code, memory, processors, and communication systems, inspired by key computer science books.
Ask about this video. Answers come from its transcript only — with the timestamp, so you can check them.
Generated from the transcript and can be wrong — check the timestamp.
Key Takeaways
- Understanding code and binary systems is essential to grasp how computers work.
- Simple communication methods like Morse code illustrate fundamental principles of data encoding.
- Electrical circuits and logic gates form the hardware basis for computation and memory.
- Bits and bytes are the core units of data representation in digital systems.
- Early computing challenges shaped the development of modern computer architecture and instruction sets.
What the video covers
- The video introduces foundational IT concepts based on recommended books like 'The Code' by Charles Petzold.
- It explains the evolution of communication codes, starting from Morse code to binary systems used in computers.
- Demonstrates encoding and decoding information using Morse code and Braille as examples of binary systems.
- Explores the construction and function of simple electrical circuits like a flashlight to illustrate basic hardware.
- Introduces binary logic, bits, bytes, and how computers represent and process data.
- Discusses logic gates, truth tables, and their role in building computational circuits.
- Explains memory elements such as latches and how they store information.
- Touches on early computer limitations and the importance of instruction sets in computing.
- Uses storytelling with characters Tim and Vera to make complex concepts relatable and easier to understand.
- Provides a historical and practical perspective on how modern computing devices evolved from simple communication methods.
Full Transcript — Download SRT & Markdown
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The book takes the honorable second place, Matthew Justice, as it really is about how the computer is working. This video is based on both of these books lying there, as well as behind additional clarifications I also had to turn to these.
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Therefore, if while viewing this film it makes you want to pin the material or to understand some deeper questions, these books should help you with this. Anyway, if you are at the initial stage of entering
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the IT field or are simply interested in the way a computer works, then you are lucky. In just a few hours, analysis of this video will broaden your horizons very much and will expand greatly. You will go from the invention of the telegraph to the device
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modern computing machine. Path, who borrowed from the progressive humanity for a couple of centuries. For more, the simple perception of the video is diluted with fictional stories from non-fictional lives that lay harmoniously between theory. Enjoy watching.
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Tim and Vera are teenagers whose homes are located next to each other, and the windows from their rooms face each other. Tim is secretly in love with Vera and believes that the best time to communicate with her is when
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parents send them to bed. Vera also likes to chat after lights out. She just likes to do things that don't find approval from her parents. And here Tim is faced with the task of how to make their
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communication more informative than simple exchanges of gestures. You can't use the phone either.
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His parents pick him up before bed. Yes, and therefore, communication should be without sounds, otherwise they will be heard and the idea will fail.
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One day he decides to take advantage of a laser pointer to look through the window and write letters on the wall of Vera's room, which she could put together into words.
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The idea didn't work out. Vera couldn't guess most of the letters. Then Tim decided that each letter will correspond to a certain number of blinks of the flashlight, where one blink will mean the letter A, two the letter B, and so on.
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Further, the offer Tim wanted to convey to Vera began with the letter Ya, and that's as many as 33 highlights. By the third letter, Vera was already losing interest and falling asleep. Tim was doing well, but Tim didn't give up. And then somehow
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once he watched a film about sailors, which signal to each other with a spotlight, sending out long and short glances. Dad explained to him that for communication sailors use Morse code. At that moment, a feeling seemed to run through Tim's body
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like a small lightning. He found what he was looking for and would soon be able to convey it to Vera, the main message of his life.
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Usually, when talking about Morse code, as signs for encoding information, it implies the use of dots and dashes in the sense that each letter of the alphabet corresponds to a set of a certain number of dots and dashes.
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Although Morse code is not related to computers, it helps to understand the essence of code, which is necessary for deep understanding of how computers work. In further text, code will be implied as a transmission system of information between people and machines. Code
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ensures communication. People use code every day when communicating. The sounds that make up words are code. Text written by hand is also a code. In computers, various types of codes are also used for transmitting numbers, letters, video. To denote a dash, Tim decides to
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use a long flashlight glow. For a point, short. Besides, there should be pauses between letters, and pauses between words should be twice as long.
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Now a simple hello will take up 64 instead of glances in the encoding invented by Tim, just 14 highlights using the Morse alphabet.
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Knowing that Vera does not have good attention and perseverance, Tim suggests that finding the letters according to the Morse code will be too much for her task. After all, in search of each letter you will have to look through the entire table.
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The decoding task for Vera is necessary to simplify. What if we group the codes? Letters in such a way that they were not arranged according to alphabetical order, but according to the number of dot symbols and dashes? It turns out that codes consisting of
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one symbol, two, codes consisting of two characters, four, from three to eight and so on.
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A pattern is emerging. Elongation of code per character leads to an increase in the number of codes, twice as large as the number of codes per character. Briefly speaking,
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thus, it can be calculated how many codes can be made knowing the maximum length. At maximum, the length of the codes is four characters, which will be 30 codes, which is practically enough for all the letters of the Cyrillic alphabet, especially if combined with ё. Well, and a solid sign with
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soft sign. Only the letter e will remain, which can be used as an exception encoded with five symbols.
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Tim goes even further and builds a tree-like structure. Now, having a set of points and dashes, it's enough to walk along the branches of the tree in searching for the corresponding letter. So, for example, the code dot dot dash will
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correspond to the letter U. Morse code is called binary because any of its elements includes one of two components: dot or dash.
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Azbukamorza is not the only way of encoding letters of a written language. More than one coding system also goes by the name of its creator. Louis Braille was born in 1809, and at 3 years old, due to oversight, he became blind from birth. His parents' birth. The boy had
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a huge thirst for knowledge and at 10 years old went to a specialized training institution for blind children. At that time, best practices to facilitate learning printing texts was considered visually impaired in raised letters. But how to write it down?
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Something about the teacher was unclear. By 15 over the years, Braille developed his own letter encoding technique that is still used today, making life easier for visually impaired people. In the font Braille, every symbol of the written language
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is encoded by one or more convex points in a rectangle the size of two to three dots. Braille, just like Morse code, refers to a binary system, since each of six points of a rectangle can take on two values: to be either
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convex or flat. The total number of combinations that can be made from six points accepting only two values equals 64.
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Thus, in total it is possible to encode 64 characters. Thanks to Tim and Vera's efforts, Vera mastered Morse code. And when it stood up the question of how Tim can help Vera pass the final exam in biology, the method of encoding information was immediately
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designated. It was necessary to make a decision only with the means of information delivery, and Tim decided that the pocket function lamp on the wall can serve as a flashlight in the room where the exam will take place.
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Let's figure out what a pocket flashlight consists of. Its main parts are battery, light bulb, switch. And all of this is connected by wires. They form the simplest electrical circuit.
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If the switch is placed in the position on, then the circuit closes and the light bulb glows. If the switch is placed in the off position, then the circuit is opened and the light goes out. The lamp in the school
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in the class works on the same principle. The role of the power source instead of the batteries is played by the substation, and the role of the switch is a switch on the wall.
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Tim just has to endure this switch to the next room, from where he will be able to send information. Having learned, Tim will be able to dictate the ticket number and Vera's answer using Morse code.
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This design is nothing more than a relative of the telegraph that found its way to industrial application in 1844. True, instead of a light bulb, an electromagnet was used.
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An electromagnet is a device that when passing through it
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there was a key optimized for high-speed work. The operator transmitted long and short signals by keeping the circuit closed. On the recipient's side was electromagnet, and upon receiving signals he attracted the closure of the circuit a metal lever that when
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when lowering and rising, it made characteristic sounds clicks. Quick clicks meant a point em dashes. This design had limitation. On long stretches the level the signal drops, so it is necessary use repeaters or relays.
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In the first half of the 19th century the relay was invented by several at once by scientists independent of each other. AND although they offered different options for it use, we will get acquainted with the relay as with a dual-use device,
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like a switch controlled electrical signal, and as an amplifier, turning a weak signal into a strong one.
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The property of the relay to operate as demonstrated the switch on his Joseph Henry's lectures on the common language experiment with two electric chains. In the first chain, let's call it small, a weak electromagnet was used. In the second one we'll call her big, strong
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electromagnet. So strong that are capable of attracting a heavy load. The peculiarity of the design was that the large chain was controlled by the weak electromagnet. When activated, the key a large chain was drawn to him.
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The big chain was closed. Strong the electromagnet became active and attracted the load. When small the electromagnet was switched off, the spring returned the key back. Big chain opened and the load fell. So small the electromagnet actually controlled
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big. This is the operating principle of a relay, as a remote electrical switch. The second important ability of the relay is work as an electric amplifier signal. As we have already discussed, the telegraph, using a signal receiver in the form of
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electromagnet, had a major drawback. When transmitting signals over long distances the distance the signal strength dropped, and it was lost. Relay installed in at an intermediate point, this was decided problem. It was very close to his entrance weak current, the strength of which was
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just enough to close the relay contacts. Through closed a new strong current passed through the contacts local power source. Like this thus, a powerful one appeared at the output signal. The relay did not amplify the current directly, and used a weak signal as a command
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to turn on a new strong signal. It is due to this ability of the relay became indispensable in telegraphy. On relay stations were installed on long lines, which refreshed the weakened signal. This allowed the transmission of telegraph messages over distances of hundreds and thousands
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kilometers. The idea that language is just code must seem logical already. But if, having met In one word, people most often draw similar images, then having encountered a number, different people most likely have completely different images will emerge.
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Given that different peoples are required to transmit information uses different languages, different scripts, and for transmission numbers most people on the planet use the same symbols. By According to historians, the numbers were invented out of the need to lead
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accounting. Was needed instrument for counting objects, livestock or registration of exchanges. Of all the most ancient numerical systems have reached us Roman numerals. Special symbols in Roman system are multiples of 5 and 10. This is connected with the fact that initially people
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counted on fingers. Even children when They learn to count, and also bend their fingers.
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The numbers we use today are can also be expressed as a quantity bent fingers on both hands.
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For example, you need to calculate apples that you picked while helping to grandma in the garden. After yours the fingers will be bent, this will be mean that there are 10 apples. And for To continue counting you need more fingers.
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Then you ask grandma to bend over one finger every time your fingers will run out when counting.
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After some time, grandma's fingers too will end on the hand. I'll have to call grandfather. He will bend one by one finger, when it's already in grandma's arms all fingers will run out. It turns out that one your finger corresponds to one apple,
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one of grandma's fingers is equal to ten of your fingers or ten apples, and one finger grandfather's ten fingers grandmother's or 100 with your finger. Grandpa's fingers express greater significance than grandma's, and therefore more yours. Let each participant
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counts correspond to the cell in which will be written from right to left the number of their bent fingers. At first yours, then grandma's, and then grandpa's.
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To find out the exact quantity collected apples, each cell needs multiply by the corresponding values, multiples of tens. The number of your fingers on both hands. Such a system the number system we are accustomed to and We use it every day, it's called
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base ten system or decimal. What if people had would there only be four fingers? Then right away after the seven came the ten, and after seventeen twenty. At the same time, despite that the entry of the tens is for
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five-fingered people, and for eight-fingered ones look the same, it means different quantities. This The system is named after the base eight.
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Let's count the number of apples would be meant in the language we are accustomed to decimal system, if I collected them four-finger family. First digit on the right means the number of units.
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The second digit is the number of folds fingers on grandmother's hand. At the same time, one four-fingered grandmother's finger corresponds to all the fingers of the grandson and is equal eight. We must multiply this value by eight. The third digit. Curled fingers
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grandfathers. One finger of grandpa is eight grandmother's fingers. So, one finger Grandfathers are 8 square fingers four-fingered grandson. Multiplying the numbers by the corresponding number of fingers and adding up these results, we get what equal to the value in the decimal system. That
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there is, despite the fact that the records are in two systems are the same, they mean different things quantity. So that there is no confusion when working with different systems, their grounds need to be clarified.
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There are systems with different grounds, but we are especially interested in base two or binary system.
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It has only two symbols: 0 and odi, where zero denotes the zero of something, and a unit is a quantity equal to one piece something. So, people with one with a finger on your hand to count the number
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the whole family and everyone will have to be called for apples neighbors. To designate one they also use the bent finger recording in the form of the unit symbol. But for designations of two bent fingers we'll have to use what we're used to
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symbol of ten 1. Let's continue the analogy with placing values in cells. Only this time for the binary system. First the cell on the right indicates the quantity units, the number of bent fingers.
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This cell can accept two values. Zero when none of the fingers not bent, not a single apple collected.
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and one when one finger is bent or one apple has been collected. In case of bending By the second finger all the fingers are gone.
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This means that now one finger The second family member must bend over. Like this the way the unit will be written in the second cell, while in the first value is reset. So, the first cell shows the number of units, the second
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cell - the number of pairs of twos. Third- the number of bent fingers of the third family member, where each of his fingers corresponds to two fingers of the previous one or four, there are 2² of the first. The fourth
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the cell by analogy reflects the quantity eights, that is 2³ and so on. For converting a binary number to decimal value in cells required multiply by the corresponding ones powers of two and the resulting values fold. The binary system has
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direct relation to computers. This is the simplest of number systems. The word bit is an abbreviation of the English expression binary digit. One bit is binary number. minimum possible quantity information, less than a bit - its absence.
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One bit can only take two values. zero or one. Well, what can be conveyed with with the help of one bit? And with the help of one bit can answer the question of where zero is will mean no, and one will mean yes. Well, well
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to convey more complex information Multiple bits can be used. Let's take a look at how bits handle transmission of information using the example of a regular product barcode. On the first look at the set of black stripes. Barcode
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can be found on every product, purchased at the supermarket. It consists of of thirteen digits. The first three digits correspond to the country of registration enterprises. Next comes the code manufacturer and product code manufacturer. There is a test at the end
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number. This barcode is scanned on cash register, thanks to which it is located the corresponding product in the database and the required price is set. There is a code in the book The secret language of computer science is described in the barcode
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US standard twelve-digit. We let's analyze the thirteen-digit barcode, used in Europe. Looks like a barcode consists of 13 digits and approximately 30 strips of different thicknesses. For reading The code for the scanner is a fairly narrow strip.
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They are made wide so that It was easier for the cashier to get into it. Well, well the numbers are only needed to make them it was possible to do it manually if the stripes damaged. Scanning from left to right,
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The computer divides the barcode into 95 sections and assigns units to the shaded ones area, and the unpainted ones are zeros. IN In bit representation it looks like this.
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The first and last three bits always have value 10. The scanner is configured according to them. He calculates the width of a stroke, a gap, and also the width of the barcode itself, since its size is different for each package.
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There is also a five-bit separator in center with the value 0110. Without it, the barcode will not be read.
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This separator divides the barcode into left and right parts. To the left side includes values from the second to the seventh, and to the right from the eighth to the thirteenth.
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Each value is encoded in seven bits. There are three encoding methods. LG R. Numbers from the right side is always encoded in the same way R. The numbers on the left side are mixed encoding and depend on the value,
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indicated in the first place of the entire code. The features of L-type encoding are the fact that the number of units in the code for any value is odd. In G encodings like the opposite, their number is even, and
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type R is the inverse of type L, which this means that in place of ones there are zeros, and on in place of zeros - ones. So, no it doesn't matter which side the barcode is scanned. The program itself
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will determine the oddness of the evenness, where The left side of the barcode is where the right side is.
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Let's look at how the values were encrypted, indicated on the barcode. This The barcode starts with the number nine.
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According to the table, the left side barcode, value from the second to seventh, encrypted using the LGг LGL scheme.
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The first value is 8 according to the L- encoding type has code 0110111. The next value of two according to The Gtype encoding corresponds to the code 001011.
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The code in the three corresponds to 0100001 and so on. The right side of the value is the eighth through the thirteenth are coded according to the R-type coding.
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It remains to be seen what it means check digit. To find it The following algorithm is used. First.
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Multiply the values from the first to the twelfth to their corresponding coefficients, namely for the values on in odd positions the coefficient is equal to one, for even numbers - three. Second.
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Let's sum up all the obtained values. Next we find the remainder of the division by 10. And if the remainder is different from zero, then the check digit is equal to the difference between ten and remainder. If the remainder is equal to
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zero, then the check digit is also zero. This whole system may seem overly complicated, but nevertheless draw a stripe with a felt-tip pen and receive goods at the cost of another, cheaper, the buyer no longer has it will work out. Let's return to Morse code. Her
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codes can also be rewritten using only one and zero. Let's mark the point unit. If we accept that there is a dash in three times longer than the dot, then the dash will be consist of three units. Pauses between
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dots and dashes are equal in length to the dot. Let's designate them as 1. Pauses between letters approximately equal to the length of a dash, accordingly, will be equal to three zeros.
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And the pause between words corresponds length equal to 2 dashes or six zeros. Now you can rewrite the Morse code, using only zeros and ones, that is convert it into bits. So, with the help of bits we can encrypt a barcode or
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Morse code, but when using most often you have to have a computer dealing with texts, pictures, music and video. Let's figure out how to use zeros and units can represent text and image. For this, let's get to know each other better
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with one concept - byte. A Byte is a group of eight battles. How an eight-bit number of bytes can take on 256 different values, starting with the value when all bits are equal zero, and ending with the value when all
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bits are equal to one. Because bytes are often are used when describing work computer, I would like to have a recording simpler than a row of eight binary digits. For a person, by virtue habits of working with the decimal system,
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it would be comfortable to use decimal equivalents that take value from zero to 255.
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But the process of converting one byte into decimal number and vice versa in the mind difficult. At a minimum, you will need paper and pencil. it will be much easier using the octal system, where each number of the octal system
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corresponds to a three-bit equivalent. Having one byte of information, it must be divided into groups of 3 bit, starting from the right edge. The last one group for complement of three bits in mind zero is assigned.
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Thus, the minimum value, which takes 1 byte will be correspond to zero in octal systems. And the maximum value is 377 in octal system.
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It seems like a solution has been found, but the problem it will start as soon as we want it to use a few bytes of information, for example, when composing sixteen-digit number consisting of of two bytes. After all, the performance
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such a number is equivalent to octal system does not coincide with octal representation of two bytes that make up This is a sixteen-digit number. This happens because when converting one byte into a number in octal system for the leftmost
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groups instead of three bits there remains only two. Therefore, when combining two bytes, when trying to get octal representation, this left group is selecting one bit of the adjacent byte, which results to an error. It turns out that in order to
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avoid capturing other people's bits, for representations of multi-byte values, it is necessary to use a reference system, in which all the numbers presented will be expressed in either two bits or four, since only then the byte will be divided into equal amounts
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bits, and encroachments on adjacent bytes will not occur during translation. A system of counting in which all numbers can be expressed in two bits, called based on 4, since such a combination can describe four different meanings, which will be matched with equivalents 0
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1 2 3. The frame of reference in which everything numbers can be expressed with four bits, contains 16 different meanings and is called hexadecimal.
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Before this we dealt with systems counting with a base less than ten. IN they used the numbers we are familiar with from zero to nine. Further for clarity we will use apples to make it it's easier to understand what quantities we're talking about
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speech. Let's start with the decimal number we are used to. systems. In it after the nine comes ten, which corresponds to ten apples.
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And in the system there are four tens based on the base comes after the three. Well, since this base four system, this entry corresponds to four apples in our the usual decimal system. IN in the octal system, ten comes after
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seven, which corresponds to eight apples in the decimal system we are accustomed to system. Well, now hexadecimal system. By analogy, ten in this system will denote a quantity equal to sixteen apples in our decimal system. At the same time, the numbers
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1 2 3 and so on up to nine in hexadecimal system are equal to the same values in the decimal system. But in the interval between nine and ten the base 16 system still needs more six designations that would cover
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values corresponding to 10 11 12 13 14 15 in decimal. These values are in The hexadecimal system is represented the first six letters of Latin alphabet.
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One byte is represented by a pair hexadecimal digits. Well, 2 bytes or sixteen-bit binary number the system will be represented by four hexadecimal system values.
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Just like in other systems, the position of each digit in corresponds to the hexadecimal system powers of the number of its base.
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In the decimal system this value is equal to 16. To convert a number to decimal the system must multiply all numbers by the corresponding values and add them together.
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In this case, if the number is expressed by a letter, use its equivalent from decimal system.
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When we say the word text, we imagine a set of sentences related to each other itself in meaning. For a computer, it makes sense doesn't matter. He only cares how The symbols are encoded. The text is available break into paragraphs, sentences and words.
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Words are made up of letters, and sentences are made up of may contain punctuation marks: period, question mark or exclamation mark.
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In addition, the text may contain numbers. To enable a computer to create, store and to read the text, you need rules according to which each symbol will be represented with using zeros and ones. One of the first such standards became Ask.
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American Standard Interchange Code information. Classic Ask defines 128 characters, each of which correspond to a seven-bit code.
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In practice, the symbol usually takes up the whole bytes, although only 7 are actually used bit. The most significant bit remains zero. IN The Aska table includes Latin letters, uppercase letters, numbers, symbols punctuation and service symbols. Later Extended tables have appeared.
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based on the aske that used the entire range of 8 bits from 0 to 255 and could encode up to 256 characters. The first 128 symbols match the classic masks, and the second half of the table is filled in
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depending on the specific version and region. Because of this, it is possible that called crocodile, incorrect display text if encoding is the recording and reading do not match, because the same code in different versions may correspond to different symbols. But
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Still, 256 characters are not enough, and use of many different encodings: one table for Western Europe, another for the East, the third for Cyrillic, and also hieroglyphs and so on.
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impractical. A straightforward solution would be to use encoding characters immediately, for example, three bytes, not one. After all, if use three bytes per character, there will be more than 16 million possible codes. Enough to cover everything languages of the world. But how to force then?
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use this encoding for those who enough symbols described Asuka standard? After all, they should instead spend one byte per character three. That is, instead of one hard You'll have to spend money on three disks.
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The disc manufacturers would only we are glad. This dilemma is solved by Uniсд, universal coding standard symbols. Its purpose is to cover the symbols of all the scripts of the world and appropriate each symbol has a unique number. This
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The standard associates code points with glyphs and names. The code point is a unique number recorded in hexadecimal system. Glyphs are specific graphic design symbol. Letters of different alphabets, mathematical signs, notes and even emoji. Names are the title or
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Description of the symbol. Glyphs and names too unique. Thus, as To simplify, we can say that Unicode is This is a huge table in which everyone the symbol is associated with a description and its own a unique number recorded in
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hexadecimal system. That is, in Unicode they abandoned the binding symbols with a specific set of bits.
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Each symbol just got its own unique number, code point. For so that the computer can record symbol, file or memory, is used special form of presentation encoding. The encoding determines how translate code point to sequence of bytes. Most
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The most common ones are UTF8 and UTF16. UTFs use a variable amount bytes from one to four. English characters take up one byte and are the same as ask. Cyrillic 2 bytes. Emoji and rare characters - 4 bytes. UtF16 operates on cells
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16 bits 2 bytes. Most of the symbols, Latin, Cyrillic, fit into one cell. But there are also those who occupy two cells.
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The picture we see on the screen is in fact, it consists of many tiny pixel squares. To to display the image, the computer must know two things for each pixel: where where is it located, what are its coordinates and what is it like
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his color. Just like symbols, colors can be encoded. For every shade assign your own set of zeros to ones.
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Let's experiment. Let's start with one bit. With his help you can only code two colors, for example, black and white. Such a palette maybe only suitable for simple text. By adding one more bit, we we get four colors: black, white,
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for example, yellow and red. Technically This is a color image but it looks so-so. Let's move on to three bits, and this is There are already eight colors. In principle, If you choose these eight colors successfully, some pictures may work
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quite readable. What if these eight combinations use for shades of gray from black to white? Smooth transitions Already better. Let's move on to five bits, which will accommodate 32 different levels gray. Much better.
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And where is this limit, after which improvements become meaningless? When experimenting with coding shades of gray from pure from black to pure white developers came to the conclusion that it is optimal use only 1 byte per pixel.
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This is enough to transmit 256 shades of gray. The thing is that the human eye is not able to distinguish more than 256 such fine gradations, therefore, increasing the accuracy, for example, up to 1024 gradations visually almost nothing
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he won't give it, but he will demand twice as much more memory. Well, what about the colored ones?
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images? Computers use this called the RGB Red Green Blue model. All the colors we see are produced by mixing these three bases components. By changing the brightness of each of from them, you can get almost anything color. Code of one color pixel
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consists of three parts. Each of these three components, red, green and blue, is encoded by one byte, then There are 256 shades. Total various combinations of shades of red, More than 16 million green and blue are produced.
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That's how many flowers we get order using the RGB model. Thus, for encoding information about one color pixel three bytes of one are required for each of the three color channels.
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In everyday life, almost everyone a person is faced with problems, related to ordinary algebra. We we add up the calories eaten during the day, We count the days until vacation and so on. IN as an operan in ordinary algebra
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the numbers appear, the union of which occurs with the help of special operators: addition, subtraction, multiplication and others. Even if you use the basic rules of normal algebras intuitively, let's briefly Let's refresh.
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Commutativity. The order of the operands is not affects the result. Associativity. The result does not depend on the arrangement brackets. Distributivity. Multiplication can be distributed into addition.
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The ABC variables are numbers. However, to get closer to understanding how the computer works, ordinary algebra not enough.
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You need to be familiar with Boolean algebra, a special system in which the operands are not numbers, but logical values of true and false, which are also denoted by one and zero or on-off.
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Boolean variables take one of these values values. Let's look at the three main ones logical operations. Logical and the result of this operation is the value is true only if if both conditions are true.
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Logical or the result of this operation takes the value true if at least one of the conditions has the value true.
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Negation inverts the meaning. From truth makes a lie, and a lie turns into truth. Just like in regular algebra, in Boolean commutativity applies, associativity and distributivity, but already for logical operations.
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Let's look at an example. Oh, my, your city. Aliens have arrived. And with the purpose joint exploration of the galactic space is offered to residents go with them. But they will take it not all. They need the following people.
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Single women working as teachers or in law enforcement agencies. Single men who are not working in law enforcement agencies. Anyone who works as a programmer. For everyone conditions we will compose a Boolean expression, in in which the names of the variables are
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the first letters of the corresponding characteristics. In the first condition the candidate must be a single woman, working as a teacher or a police officer, then there are three conditions to be satisfied.
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to be a woman, to be single and to have one of the two named professions. So how the three conditions mentioned should run simultaneously, they are connected logical and at the same time the third condition has a fork. The candidate can be either
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a teacher or a police officer. To be carried out at least one of these two must conditions, so they are connected logical or check for performance is a given condition.
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For example, how it will be executed, if a single female geologist comes. The first two operants take on the value true. Let's write them as units. Let's calculate the value of the third operand. Geologist no is neither a teacher nor a policeman.
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Therefore, both operants accept value false, zeros. Their overall result will also be zero, since logical or yields truth as a result only when when at least one of the operands has the meaning is truth. Now the general condition
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It looks like this. The final value of this conditions zero, since when using logical and, in order to obtain the truth, both operants must have a value true. Therefore, despite the fact that the first solution and the result will be true
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unit, then when solving the second one and he will change to false or zero. This the candidate does not meet the requirements condition.
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The second condition is similar, for with the exception of the conditions of the profession. Candidate shouldn't be a policeman.
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This condition can be written using negation, logical not. Thus, If the candidate is a police officer, the logical answer is no.
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transforms this meaning from truth into lie. And if the candidate is not police, logically does not pay attention to this meaning into truth. The third condition is the most simple. It is always performed when the candidate is by profession
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programmer. All three conditions are connected by the operator or the candidate passes the selection if at least one condition from is met three.
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After the aliens' proposal It was announced that the city's residents were divided into two parts. Some demanded to be driven away oval-headed, while others lined up in queue to the spaceship. Those who wish It was so hard to change my life radically
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so much that the question arose: how automate the selection process, excluding long conversations? It would be It is ideal if the candidate independently in case of a positive answer to the question put to him moved the corresponding switch in
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position on. And based on the results these switches, if the candidate comes up, the light comes on and the door opens The spaceship opens.
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In order to construct such a device, Let's figure it out as best we can with people we already know us with a light bulb, a battery and move the solution with switches logical operations from paper to electrical circuit. Let's agree that
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the meaning of truth on paper will be correspond to the state of the chain when the light bulb is on, the meaning is false when the light is off. Let us denote switches with letters A and B. Let's accept them
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value in the on state for truth, and turned off for lies. Then the implementation of the logical and will be their serial connection, because the light bulb will only light up when when both switches are on, that is
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take on the value of truth. Implementation logical or will they be parallel connection, since then to turn on It's enough to turn on at least the light bulbs one switch. That is one of conditions A or B must be accepted
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the meaning is truth. Using understanding, what is a series connection switches perform logical operation and, a, parallel logical operation or we can collect electrical circuit that will replace expression for selecting candidates.
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The switches in this diagram are labeled letters that correspond characteristics of candidates. If the candidate has this characteristic, he must translate switch to the on position.
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Using the distributivity given the conditions of the consequential circuit can be simplify, take out the characteristic of cold outside the brackets. But even despite this simplification remains seven switches, which the candidate must operate.
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The probability of making a mistake is very is great, so we will see further how you can reduce the amount switches up to four.
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Let's move the switches to a separate place tablet and we will designate them K1, K2, K3 and K4.
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Basically, each switch is one bit, since it has two states. Maybe be on, may be off. All candidates are either men or women. To transmit information about this characteristic requires only one bit or one switch.
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Switch K1 will be responsible for the floor. If the candidate is male, then The switch must be on. If female, then switched to off state. Switch K2 will be be responsible for the status. For accuracy definitions of this characteristic
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any candidate is also enough for one bat. If the candidate is single, the switch must be in position enabled, otherwise disabled. Of the remaining conditions remain for the profession: teacher, policeman and programmer. Residents, no having the listed professions,
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are engaged in other activities. It turns out that, regarding professions, everyone candidates can be divided into four groups. By connecting two switches K3 and K4 together will make two bits. And this is how once four options: 001 10 1. Let
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option when both switches K3 and K4 are turned off and have a value of 0.
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Other activities are relevant. option when both switches included, value 1. Programmer. Option when only is enabled Switch K3, value 10, teacher.
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Well, and when only the switch is on K4, meaning 01 policeman. Like this Thus, we reduced the number switches from 8 to 4. For implementation circuits that work with four switches, let's get acquainted with logic gates. Logical a valve is a device that
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takes one or more logical inputs, the value is zero or one, and outputs one logical output, defined logical operation, such as and or not and others. The output also takes on the value zero or one. There are several
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methods for implementing logic gates, and one of them using a relay. Previously we used a relay to transmit the signal over long distances. Now us interested in the possibility of control switch using electricity.
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In such a circuit, the electromagnet-relay and the light bulb is connected to different sources nutrition. When the circuit is closed with it is activated by an electromagnet and attracts the switch, closing the circuit with a light bulb and it lights up. Place, in
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in which the electromagnet attracts the key the circuit in which the light bulb is located, Let's call it a contact. If we accept that the presence of voltage is a logical one, and its absence is zero, then this
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The relay transmits the signal without change. If if there is one at the input, then there is one at the output unit. If the input is zero, then the the output is zero.
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A logical element in which the output the signal coincides with the input, it is called buffer. The buffer is indicated by a triangle, whose input signal is fed to one of the sides, and the output is removed from
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the opposite vertex. The buffer can be used, for example, to delay signal or to amplify it, as it is was done in telegraph technology. Possible and another scheme. The light bulb stays on for now the circuit with the electromagnet is open. How
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as soon as it closes, the relay opens a chain with a light bulb and it goes out. Such the connection is implemented by the inverter, performing the role of logical no. He inverts logical signal. If the input is
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zero, then the output will be one and vice versa. To indicate the inverter The following symbol is used. At the exit the relay does not necessarily have to be the key chains with a light bulb. This could be it
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switch from another relay. Like this Thus, the output of one relay can serve as an entrance for another. At activation of the electromagnet of the first relay the second thing will work too, which will ultimately will lead, for example, to the inclusion
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light bulbs. The outputs of the two relays can be connected in series. In this case the only way to light a light bulb is activate both relays. Keys in dots the contacts will close and the light bulb will come on
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will light up. So consistent the relay connection implements logical the AND operation is called the AND gate. For its designations on diagrams are used special character. This symbol has Usually two inputs and one output. Mentally We can transfer our diagram with the light bulb
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for this symbol. Then there will be at the entrance two switches, and a light bulb at the output.
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When the keys are closed one after the other, nothing happens. does not happen. The light will only come on when both keys are closed simultaneously. The result of closing the key is the appearance of voltage at the input, that is
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change the logical value from zero to unit. Then the behavior of the valve can be describe with a truth table.
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The number of inputs of the valve and can be more than two. For example, you can use three relays, the outputs of which connected in series. This too will be reflected on the symbol. He will have three entrance. As you might guess,
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parallel connection of the outputs of two the relay implements a logical operation or and is called a valve or in such a case when the relay is connected, the light comes on, if at least one of the keys is closed
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together contacts. The valve or has its own symbol for designation. It is different from valve symbol and what it has rounded shape from the entrance side.
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If the valve has two inputs, then it can be in four logical states depending on the combination input signals. Having an idea, How a valve and a vent are constructed inverter, let's get back to building the circuit to select candidates. First
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switch in closed state matches the male candidate. IN We use an inverter for an open woman.
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Then, when the input is equal to one, when the switch is on, the output is with the designation M a man will also have the value is one, and the output is G.
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If the switches are open, then there is the input value is zero, then the output M is also will have a value of zero, and the output G unit. Solution for single or not single similarly.
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Let's move on to professions. We divided everyone candidates for four groups: teacher, policeman programmer etc.
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activity. There are two switches, each of which takes two states: on-off. Various combinations of these states keys uniquely identify each group. For clarity, let's draw lines from each state of each key to relevant profession. For designations that the candidate is,
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for example, a teacher must include switch K3 and turn it off switch K4. It is used logical AND. Therefore, the signal is The teaching profession will serve as a way out valve I. But in order for the input
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logical gate and get one, There must also be two units at the input. In our case, we have one so far one and one zero. Let's change the drawing and at the place where switch K4 is open, We use an inverter. Then when
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switches K3 and with switch K4 turned off at the input The fan and the teacher profession are presented in two ways units, and the output will also be unit.
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Let's replace the drawing of the K4 key with a diagram. We also use a bundle inverter with with the K3 key and add a logical and for every profession.
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Let's check the functionality of this circuit. For example, we turned off the K3 key and turned on the K4 key. Since at the input of the key The K30 inverter converts the signal into one and sends it to the logical
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valves associated with the police and other activities. There is one at the input of key K4. This signal enters the profession of a programmer and police officer. As a result, at the entrance of all logic gates are supplied in two
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signal. And only at the logic gate, related to the police officer, they are both equal units, resulting in the output there will be one, while everyone else the rest of the output is zero. We're checking. Yes, Indeed, that's how it was intended. For
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identifying oneself as a police officer The candidate must switch K4 switch to the on state, and switch K3 to off.
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The resulting circuit, in which two the switch forms one active the exit from four possible is called decoder of two lines into four. U it has two inputs and four outputs, and in each moment in time is active only
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one exit, the one that matches input combination. So, for now we have only drawn a diagram for the remote control, which, using four switch, will give us enough number of output signals, allowing to solve the selection problem candidates.
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Using gates and or and inverter, Let's redraw the diagram for seven keys. Instead of the keys will be input signals, taking two values: zero or unit.
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All that remains is to connect the input signals the resulting circuit with output signals remote control. Remaining outputs from the remote control Let's just ignore it.
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Let's check the circuit for functionality. For example, the candidate is a man Switch K1 is on. Single Switch K2 is on. By profession loader. Keys K3 and K4 are turned off.
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Since he is not a policeman, the inverter converts this signal from zero to unit. And to the input of the AND logic gate two units are supplied, so at the output He also has a unit. This output is simultaneously an input to a logical
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valve or, for which it is enough only one unit at the input, so that get the output one. Exit valve or is the input of the next gate I, which also has an output the result is one. Next valve
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or also gives one as output. IN As a result, the light comes on and the door closes the ship for this candidate will be open.
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For the sake of completeness, let us consider another several logic gates. Valve or is this not a logical element of behavior which is opposite to the valve or on it can be represented in a relay circuit as follows. Initially the chain, in
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which the light bulb is located is closed. The outputs of two relays are connected sequentially, and upon activation electromagnets of the relay they open light bulb switches. With this When connected, the light only lights up when in the case where both electromagnets are not
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active. In other words, while at the entrance two zeros, the output is one, but if activate at least one electromagnet, the light will go out. Valve and not logically opposite to the gate and Relay outputs are connected in parallel.
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The light bulb stays on as long as at least one of the the electromagnets are not active and go out only if both electromagnets are in an active state. That is the output will be zero only in the only case when there are two at the input
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units. In all other cases, the output will be one. The basis of a computer's operation is addition.
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numbers, because all the others arithmetic operations. Subtraction, multiplication and division can be reduced to sequences of addition operations, sometimes using the add-on shifts. The purpose of this section is to build adder. An adder is an electronic device.
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a device that accepts input two numbers and returns their sum. We will collect it, using the simplest elements: switches, relays and light bulbs. IN in the decimal system we can easily make an addition table. If take a closer look, then each received
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the value can be divided into two components: units place and tens place. This one the table can be divided into two tables: table for the rank of units or sum and table for tens place, carry.
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Attempts to build an addition device numbers in the decimal system will take us to dead end, so it's easier to go to binary a system where there are only two values: zero and one. This fits perfectly electrical circuits, after all
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switches, bulbs, wires can accept only one of two states. Thanks to these circumstances, it is possible to build a device that adds binary numbers numbers, it will be easier, and to understand it the work more clearly. Let the role of devices
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to enter numbers, the sum of which it is necessary to find, they will perform switches.
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The first row of switches will be relate to the first term. Second the series is responsible for the second term.
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The switch position is the same as position of the number value. To indicate units switch required switch to on state for zero to off.
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The role of the output of the addition result will be make a row of light bulbs. Included the light bulb corresponds to the unit, switched off zero. A row of light bulbs on one the position must be longer than the rows
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switches, since the output in case must accommodate the necessary a number equal to the sum of two maximums numbers that can be obtained on at the entrance. Implementation of our adder Let's start with the addition table, but only for
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numbers of the binary system. We will also highlight from it has two tables: a sum table and a table transfer. Let's display the tables on the screen dependence of output signals on input signals when using different logic valves. For greater clarity
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Let's rewrite these tables in a different form. A and B act as input signals. We we see that the column value is carried over completely coincides with the meaning, which we would get if we used valve I. And here is the value of the sum column
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equal to units only when both are weekends signal from the fan or both the fan and not are also equal to units.
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So, if both of these signals are fed to the input of the valve and we will get the desired result. This circuit consists of three valves.
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is called an exclusive or gate has its own designation. It's similar to designation of the valve or and differs from him with an additional curved line sides of the entrance. So, when adding two binary numbers can be used
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the next two gates, where the sum digit is set by the output of the exclusive valve or, and the carry bit is the output of the valve And. This circuit is called a half adder.
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Let's simplify it. Our goal was to make adder. Why did we succeed? some kind of half adder?
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Let's consider the addition of two-digit numbers in binary system. For example, 1 and 01. On In the first step we add up the values from right column. Adding two units, we will write zero in the result and one
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keep this in mind for the next category. Well, here, of course, we can take advantage of what was received half adder, which has at its output the sum will be zero, and the output of the carry unit. Next we have to add
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the value from the next column, to which will additionally add value from transference. But with the half adder this the trick won't work. He only has two inputs that we use for two values. From the corresponding column.
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To add three binary digits you will need one more half adder, one from the inputs of which we are just using for transfer. And we'll feed it to the second entrance.
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the value of the sum from the first half adder. As a result, we get three outputs: output sums of the second half adder, output carry of the second half adder and output carry of the first half adder. On
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output from the sum of the second half adder we we get the value that we enter when adding numbers in a column, in the corresponding category. Left understand the meaning of hyphens both half adders.
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Let's use it for fun with one half adder and let's see what it will work out. Using various combinations that we can submit for input of this circuit, we will only get four output options: 00 100.
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By the way, we would have received the same options simply adding three binary digits systems in various combinations.
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An important observation is that carry output of the third half adder always zero. It turns out that no matter what values were not supplied to the input of this systems, first and second carry outputs the second half adder at the same time
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never take on values equal to units. At the same time zero, yes, but if some carry output is equal to one, the second will be equal to zero.
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To simplify the circuit, the third half adder can be replaced with a valve or thus, using two half adder, we get the full adder. Also, for simplicity, we will make it simplified diagram. The full adder has three entrances, one of which is the entrance
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carry obtained by adding digits previous order. He has the same as The half adder has two outputs. For addition of two-four-bit numbers four must be used adder. The carry output of each of adders is the input carry for later. Since when adding
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least significant digits of the incoming there is no carry yet, this adder is replaceable to a half adder. Let's connect the switches our device to the inputs, and the light bulb to corresponding to the sum outputs. Exit carry of the last adder also
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will be connected to the light bulb. Let's check the performance of the received device.
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Let's add two four-digit binary numbers systems. For this purpose, each switch we will convert the corresponding units into on state. Light bulbs that lit up, correspond to one, others zero.
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If in the circuit instead of a half adder to return the adder back, then by We can already copy this scheme add eight-bit numbers. For this carry output of the last adder It is necessary to short-circuit the circuit instead of the light bulb
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carry input of the first adder added group. Next you can create a device that will fold already sixteen-bit numbers. We will stop on an eight-bit adder, let's simplify it scheme for further work.
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In the schemes we have considered earlier, electromagnet relay and switch the contacts had different power sources, let's combine them into one chain. In such a chain two switches. One is controlled external influence, for example, manually, another electromagnet connected to
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of the same chain. When you turn on the first one the switch closes the circuit, the light bulb lights up and the electromagnet attracts the movable contact of the second one towards itself switch, which opens the circuit.
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The light bulb goes out, the electromagnet is de-energized, the spring returns the contact to its place, closing the circuit. The process repeats again and again. Closing and opening of contact the relay is accompanied by a characteristic clicking or rattling sound.
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This device is without a light bulb. used as electromechanical zoomer. If to the second switch attach the hammer, and underneath it install the bowl, then you can get an analogue of the much-loved old school the bell announcing the end of the lesson.
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Let's remove the first switch from the circuit. It turns out to be a closed system in which closing the circuit causes it to open, and opening again closing.
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This behavior resembles work inverter, only here the output is supplied back to the entrance. This chain is called vibrator or oscillator. His the peculiarity is that it closes and opens the circuit without external impact.
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You may see a contradiction here, because the inverter produces the opposite signal, and here it seems to be an input and an output are equal.
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In fact, the delay in explains everything relay activation. Signal passed inverter, in this case a relay with changeover contact, returns to the input already has the opposite value.
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The delay is determined by time triggering and releasing the relay, which depends on its design. If construct a graph of the output dependence signal from time, it will turn out periodic form. The signal is constant changes from zero to one and back.
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An oscillation cycle is an interval in which during which the vibrator output changes and then returns to initial state. The time that takes one cycle, called a period oscillations, and the number of such cycles in second frequency. Purity is measured in
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Hertz and depends on the characteristics specific relay and circuit parameters. IN a vibrator that works on its own, of little use. However, it is important part of automation, since in any the computer has a vibrator of a certain type, providing
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synchronous operation of all components computer. Let's consider another scheme, in which two relays are connected so that the electromagnet of the first relay controls contact that powers the electromagnet the second rail, and vice versa. Logical the model of this scheme can be represented in
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in the form of two inverters connected crosswise. The output of the first one is fed to the input of the second, and the output of the second to the output first. This configuration forms feedback that reinforces current state. When power is supplied
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the circuit will spontaneously settle into one from two states and will remember it until until external influence will change it. All information about the condition the system is contained in one variable Q, until a change occurs. Like this
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Thus, the design is an unstable cell capable of storing one bit of information. In its pure form crossover inverters in real are almost never used in devices, because they do not have control inputs to change the state. In practice, they
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complemented by set and reset inputs, receiving, for example, triggers. One of the simplest schemes that allows control the state variable Q, is RSGER. It got its name from English words reset and set. RS-trigger can be assembled on two valves or not
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Let us recall that the output of the valve is not equal to or unit only when all of it inputs are zero. When submitting at least one unit at the output will be zero.
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Let's look at all four possible ones combinations. inputs R and S. First case RS S0. On the top valve or not a unit is supplied, which means its output is Q is equal to zero. Both lower and line inputs
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are equal to zero, so its output is unit. Second case. R = 0 Sни. On the lower valve or the unit is not supplied, This means its output is zero. Both entrances the top and the line are equal to zero, so Q
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equal to one. The third case. Both entrances are equal to one. When submitting a logical units at both inputs, both outputs take the value zero. However, because of different signal propagation times in the elements it is impossible to guarantee,
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that upon subsequent reset of the inputs to zero both outputs will be set to the correct steady state. Even short delay on one of the inputs may lead to the fact that the trigger will be in an unpredictable state
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state, so this mode is considered prohibited. The fourth case. Both inputs are zero. In this situation we can't determine what the outputs of both are valves, since in order to determine them, It is necessary to know their meaning. Closed
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not quite a circle. Let's assume that output Q has some value, established before the fourth case. Q previous. It can take one of two values 0 and 1.
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Let us consider the variant in which Q the previous one is equal to zero. Then the bottom one the valve does not have any inputs two zeros, which means the output is one.
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Having one unit at the input, the upper the valve and the output line receives zero.
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It turns out that the value of q at q before the previous one equal to 0 is also equal to zero. Option the second, in which Q is equal to the previous one unit. Bottom valve or not has one zero and one as inputs
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one, which means the output is zero. The top valve or not at the inlet has two zeros, then the output Q is equal to one, that is, the same value as Q previous.
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It turns out that when the inputs R and S accept value, the output value Q depends on previous value of Q. If Q was zero, it will remain zero. If there was one, one will remain. That's it trigger memory. While the inputs are zero,
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the circuit stores its state. Knowing the current output value can be make a conclusion which of the inputs was the last one under voltage. Let's sum it up.
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Applying a unit to S sets Q equal to one. Feed unit per R resets Q to 0. When R is 0 and S equal to 0 the value of Q is preserved. Table the truth value of the RS trigger can be expanded,
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supplemented with the value of the previous state output Q. In simplified form, the RS trigger is depicted as a rectangle with two inputs R and S and two outputs Q and Q underlining.
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The stringer is capable of storing one bit. information. The question arises why The feedback circuit is something else entirely.
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remembers? The secret here is that the output of one valve goes to the input another and vice versa. Such a cross The connection reinforces the current state.
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Even if the R and S inputs are zero, the circuit remembers what signal was given last, and retains this value.
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It is thanks to feedback it turns out to be memory. The RS trigger is simple in design, but it has There are two noticeable drawbacks. Firstly, it has a forbidden state. If send signals to both at the same time
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input, the result becomes undefined. The third case when signals R and S are equal to one. Secondly, It reacts to input changes all the time.
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the time while the signal is being given. The problem is the fact that in real circuits the signal on inputs do not always change perfectly sharply and clearly. He may tremble due to noises.
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or interference or switching too much fast. If this happens at that time the moment when the trigger is still in in the process of establishing a new state, he can record multiple changes instead of one. As a result, at the output instead
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the planned value will appear random result. Let's equip an RS trigger functionality that allows you to accept data only at a certain point in time. For To do this, we will install two in front of the R and S inputs
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valve I. One valve receives signals S and A, the other is R and A. Signal A is a signal recording permissions. His meaning is to manage moment of recording. While A is zero, the outputs of the screws I will always be zero. And
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the RS trigger inputs remain inactive. When A is equal to one, the circuit works as follows: regular stripper. If S = 1 and R = 0, the output Q is equal to one. If R = 1 and S =
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0, Q is reset to zero. After recording A can be reset to zero again. Trigger will retain its state, and the changes there will be no signals on R and S influence. Until the next recording resolution.
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In order to get rid of unacceptable state when S and R = units, we will replace them with one input.
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Signal D, date, data. Information from D will flow to the lower valve I. A to the input of the upper valve and we will feed inverted signal D. Input A at Let's rename this to a clock. In this
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In the context of the input, the clock denotes synchronization. The resulting circuit is called a delatched circuit.
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level-triggered. The term latch means that the circuit locks one bit of information and stores it it for further use.
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Level triggering means that output Q repeats input D all the time until the signal at the clock input is active level. For example, equal to one. When the clock is zero, the latch closes.
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The output Q remains unchanged. Even if input D continues to change, Sometimes it is necessary for the output value to be Q did not change by level, but only in the moment the clock signal transitions from one state to another. For example, when
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transition from zero to one positive front. For this a D-trigger is used, which is built of two D latches, leading and driven.
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To create a de-trigger we use two Dlatches. The left latch will be the leading one, right driven. Output signals of the leading We will designate the latches as Q1 and Q1 prime driven through Q2 and Q2prime.
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Signal Q1 from the master latch comes to the input D of the slave latch and goes directly to one of the entrances to its lower valve I. to the upper valve And the same The signal comes through the inverter. But so
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as signal Q1stroke, driving the latches, is opposite to the signal Q1, then the circuit can be simplified to one inverter, connecting the output of Q1 prime to the input the top valve and the slave latch.
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For better readability of the diagram Let's turn over the leading latch. We will also increase the distance between valves, leading latch. Exits the leading latches are the inputs for slave latch valve. Clock signal controls both latches, but before
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it passes through the entrance to the leading latch via inverter. Because of this, the presenter the latch will be open when the clock is equal to zero. The slave latch will open slightly when a clock equal to one only for that,
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to get the value from the leading latches. Thanks to this design, the output is fixed to only one value D, the one that was at the time of the front clock signal, that is, in our case transition of the clock value from zero to
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unit. This design eliminates The latch is transparent and the output is responsive only on the transition of the clock value.
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Let's look at how the de-trigger works step by step. To do this, we add to each of the outputs bulbs that will light up when value equal to one. To inputs D and We'll install switches that will be transmitted as a signal either
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one or zero. Wires bright green color conveys meaning equal to one. Dark green wires colors carry a value equal to zero. U The meaning of the red wires is not defined.
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The leading latch is set to zero. transparent. The current one is written into it value D, that is, the output value Q1, the leading latch is equal to the value of D.
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The light bulb is powered by the Q1 signal, lights up only when input D is connected one unit is served.
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Next, let's look at what happens when changing the clock value from zero to unit. Switching the clock value. So What is the meaning of the key to the leading latch?
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comes through the inverter, it is closing. At the same time, to the slave A unit is supplied to the latch from the input of the clock.
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It opens and takes on meaning with output of the leading latch. In our example output Q1 of the leading latch at When switching, the clock is equal to one. That's why at the output Q2 of the slave latch we also
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we get one. Change signal to input D, while the signal at the clock input is equal to units, does not affect the outputs of Q1 and Q2. The output of Q1 changes only during transition of the clock along the front, in our example
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along the positive front, that is, when transition from zero to one. Let's return the clock value to zero. It's opening the leading latch, and the signal is transmitted to it D. In our case, at the moment of transition
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the value of signal D is zero, therefore the value of Q1 changes to zero. Led by the same the latch closed. These changes have already happened to her.
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do not concern. And no matter how the signal changes d, the slave latch stores the signal, received from the leading latch at the moment signal transition to the lock from zero to unit.
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In the diagrams, the D-trigger is designated with triangular arrow at the entrance of the clock.
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Just a triangle, triggered by positive front. Triangle with circle, triggered by negative front. So, D triger not only stores one bit of information, but it does it exactly at the moment of the clock front signal. Thanks to this, he turns into
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into a controlled memory cell. Bit is updated only when it is necessary, ensuring stability predictable operation of components computer.
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Let's transform the d-click. Let's replace the input names and exits to more relevant ones.
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Output Q is renamed to out, which means data output. Input D will be renamed to in.
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Data entry. The signal that controls the moment of recording, we'll call it W. From the word WR right. Write it down. When W is equal to one, the value from the input in is transferred to the output out. When W = 0, the latch is closed and
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the output value does not change. Back the output Qprime in this circuit is not is used. It is only needed for internal workings of the latch.
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We assume that the recording signal is usually is equal to zero. In this case, the signal is on The input in does not affect the output out. For storing the value from the input in The latch needs to be entered into the entry
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one, then zero again. At the moment, when the input W is equal to one, the value latches on the output out duplicate the value at the input in, and after switching to zero will save it. For the opportunity
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scaling the resulting latch The image can be simplified. This The latch locks one bit of information.
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If we combine, for example, four of these latches, you'll get a small group memory that already stores the whole four-bit value. Such The combined latch contains four input in, four outputs out and one common login entry. To record four-bit
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values in such a latch input write switches from zero to one. Data from the inputs in will be displayed at the outputs out.
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To save them, the entry state is recorded. switches back to zero. Let's simplify image of a four-bit latch. On at the input in and output out we indicate the number, indicating their quantity.
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Let's consider another layout method single-bit latches when there are the need to write and read instead one four-bit value. four individual single-bit values during some period of time.
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As data recording and storage cells the same ones will be used single-bit latches. The task is worthwhile simulate two logical blocks, the first of which controls the recording data, decides which latch write a bit. The second block is engaged in
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reading, selects from which latch read data. Let's start with the first block. The input is supplied signal that should be recorded in one of the latches. Which one of the latches exactly?
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we choose ourselves? Below the post we we mean duplication of meaning with input in at output out. This is happening in in the case when the input is unit. If we combine the inputs of all latches, then to write to the desired cell
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data submitted to this single entrance, at the same time on her entrance WR right unit must be supplied. Like this Thus, the first block should control write signal to each of the cells. If we we want to record a signal, for example, in
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the second latch, then to the second input latches from the logic block should unit to be served. At the same time on all inputs of the remaining latches are fed zero. Doesn't this remind you of anything? We already
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solved a similar problem when selecting people to conquer space in six criteria, having only four switches. We solved that problem, using a two-line decoder on four. With his help, using two switch, you can precisely select one the desired exit from four possible ones.
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We will use it in this case too. We will give The switches are named S1 and S2. The first one the latch will be recording, when both switches are off, then there is their value equal to zero. For this
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their signals must pass through an inverter. The entry will be in the second cell produced when switch S1 zero is supplied, and to switch S2 unit. Only current passes through the inverter signal from switch S1. Further logic continues.
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We have one more signal that controls the recording moment. The entry must happen exactly when it is equal unit, and not all the time, while some from the combinations S1 and S2 supports one from the outputs active. This signal also
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we will apply to all logical and left blocks as a third signal. Now for so that the latch opens for recording data, in addition to the correct combination switches, the recording signal must have a value equal to one. Let's check
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the resulting scheme. For example, at the entrance one unit is served. We want to record this value in the third latch. For this Switch S1 must be on. S2 turned off. To write to the input Wт unit.
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After the data has been recorded, to ensure their safety, input W is switched off.
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Let's move on to the second block, block readings. His task is to choose signal from the required latch and the output of this signal to the common output of the circuit. Task the opposite of what we solved with the left one
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block. To solve it we use four-line to one selector. Let's figure out how it works. Just like in the decoder, to select one line switches are used. Let's call them S3 and S4. At the input of the valve I are supplied
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three signals. Two signals are sent from switches. The remaining signal is- output signal out, corresponding latches. The outputs of these valves are inputs for the valve or, in fact, a selector does not select the latch itself, but activates it
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one of the valves and to which it is connected output of the corresponding latch.
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Combination of switches S3 and S4 determines which particular gate will be open. Thus, choosing, for example, combination of switches corresponding third latch, the only AND gate, at the input of which two units will come from the switches S3 and S4 will be the third AND gate.
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The value of its output depends only on what value is supplied to it the third input, that is, stored at the output out of the third latch. If it is zero then the output will be zero. If it's a unit,
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then the output value is also one. A what about the outputs of the other valves? So as any combination of switches S3 and S4 makes only one gate active And, in our example, this is the third gate AND,
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then at the output of all other valves I, no matter what the value stored in appropriate latches, there will be zeros and they have no effect to the common outlet of the valve or the right one block.
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Its output is equal to the value in the third latch. Let's make one more adjustment.
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Since we are considering the simplest an example where at one moment you can either read data from memory, or there is no need to write it down use four switches. Two for the decoder and two for the selector. They
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duplicate each other's functions. Their task - just select the desired latch. Let's reduce them to two. These switches are called an address. In this case, this a two-bit address uniquely defines, which latch are we referring to? Decoder at the address selects one line for
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records, and the selector one signal at reading. Both are controlled by the same a combination of switches that points to the desired memory cell.
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Memory can be random access and consistent when used which for reading the value by a specific address is required first read all values from previous addresses. The configuration considered The latch is a random access memory access. Let's simplify the image of this
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configuration capable of storing four individual single-bit values. Her too can be designated as a 4 by 1 RAM array, in which can store 4 bits information. To get an array, in which can store 8 bits, eight latches must be used and
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three-bit address, that is, to use at least three switches, since with the help of such a quantity of them it is possible organize a separate one for each latch access. For 16 bits, respectively, 16 latches and at least four
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switches. and so on. If so use the same addresses and input signal W for different arrays memory, for example, for two 4x1 arrays, the result will be a 4x2 array, then there is an array that stores four values, each of which is 2 in size
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bat. Similarly, it is possible to construct larger arrays, such as 1024 8 bit. This array has at least 10 switches for addresses and eight inputs in and out. Such an array allows you to store 1024 bytes, 1 KB.
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The memory collected in this way cannot be implemented using a relay. First of all, relays are bulky mechanical devices. For storage even a small amount of data hundreds of relays, kilometers would be required wires and a huge amount of energy.
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Secondly, each relay has limited response speed. At at each switch the moving part should have time to pull itself together and return to place. On a large scale this leads to to significant delays. Over time relays wear out, contacts burn out,
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the springs lose elasticity, and the circuit stops working stably. Next a step in the development of electronics was use of vacuum electron lamps. From them, as from the relay, it is possible assemble logical elements and, and, linearly, and then adders, decoders and
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selectors. That is, everything that we built using relays, it is possible implemented without a single moving part.
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The lamp does not contain any mechanical parts, but controls the flow of electrons, thanks to which switches thousands of times faster relay, and it's also silent. In the mid-20th century centuries lamps have already been actively used in radios, televisions and
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amplifiers. Engineers moved this principle and in computing technology. It was the lamps that became the basis of the first electronic computers. However, the lamps There were also serious shortcomings. They consumed a huge amount of energy and gave off a lot of heat. Big ones
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the computers were literally fried air. In addition, lamps are often burned out, and there were thousands of them, and the service turned into a daily routine replacement of burnt-out elements. Yes and they still took up just as much space,
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why one computer could be the size of an entire room. It's interesting that their main advantage is high speed was not a decisive factor at that time roles. The main bottleneck remained program reading speed punched cards or paper tape. Nevertheless,
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Lamps were an important evolutionary step. They allowed engineers to get rid of mechanics and go to full electronic computing. This opened up the path to new, more reliable and compact solutions. And the next one is like this the solution was the transistor,
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a semiconductor device that performs that the same function as a lamp, but hundreds of times smaller, more reliable and more economical. He became a real revolution in electronics and changed the face of computers forever.
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A transistor, like a vacuum tube, controls electric current, but does it is not by means of heating and flow electron vacuum, and with the help of semiconductors, materials that can change their conductivity.
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Semiconductors, for example, Germany and Silicon got its name not because they conduct current halfway worse than, for example, such a conductor, like copper, but because of their conductivity can be controlled using impurities and electrical voltage. Transistors There are bipolar and field ones. To
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understand the general principle of their operation, Let's consider a bipolar transistor of the type NPN. It has three terminals: base, collector and emitter. One can imagine that between the collector and emitter are located electronic key. Manage this key
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is carried out by applying a weak current to base. If there is current at the base, the transistor opens, current flows freely from collector to emitter. If there is current at the base No, the transistor is closed and there is no current
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passes. In other words, the supply of current to the base sharply reduces the resistance between collector and emitter, and its absence creates a barrier equivalent to open circuit. Important property transistor is that for its control requires very little current, and
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the current it controls can be in the tens or hundreds of times more. By connecting two transistor in series, it is possible implement the logical operation and, and when parallel connection logical operation or transistors have a whole a number of advantages: miniature size,
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reliability, energy efficiency, high switching speed. But still not less, despite all these advantages, There was one problem left. Every the transistor was connected to others components capacitors resistors, other transistors manually. Even a simple circuit required tens or hundreds of parts, connection
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which had to be soldered manually. This is not not only slowed down the assembly process, but also made every scheme potentially unique and increased the likelihood of errors and refusals. So the next step was invention of integrated circuits.
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An achievement as significant as itself transistor. In the late fifties the idea came up to combine several transistors, resistors and conductors on one tiny flint plate.
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This is how the integrated circuit or chip. Now instead of connecting elements by hand, the whole scheme was manufactured entirely at once crystal. This gave fantastic advantages. The schemes have become much less. faster due to short connections, cheaper due to mass production
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production, more reliable. That's right, uniting millions, and then billions transistors on a single crystal, the result was a microprocessor, the brain of a modern computer.
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Memory stores data and instructions, which the processor performs. Every the processor supports a set of instructions, through which they are realized programs of varying complexity, even those which had not yet been written at the time processor development. These instructions
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are very simple in themselves and perform fundamental operations. For example, memory access, reading and writing.
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Arithmetic operations, addition, subtraction multiplication division logical operations and or not, tracking the progress of the program, transition to a certain part of the code, call under programs and so on. The processor consists of from many components. Let's get acquainted with
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three main ones: arithmetic-logical device, control device and registers. Registers are super fast internal processor memory. They temporarily store data and addresses that the processor is using right now for execution of the current command. For example, numbers to add or address
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next instruction. The registers are working much faster than RAM. The register size is correct processor bit depth.
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Arithmetic logic unit performs mathematical and logical tasks operations. Alu is complicated combinational logic circuit, at the input which receives values and code operations indicating what is needed do: add, subtract, compare and and so on. At the exit, Alu gives out
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result of calculations. Device management carries out general management processor operation. Processor operation - it's a continuous repeating cycle, known as the sample-decoding cycle and execution. Since it is executable the program is stored in RAM, control devices require an address,
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by which it is necessary to count from memory the following instructions. For this one of processor registers are used for program counter pointing to the address instructions to be followed next. Control device reads instructions from RAM memory and places it in a special
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register, command register. Next decoding. Built-in decoder instructions analyzes the read binary code and determines the type of operations: arithmetic logical transmission data or move to another part programs. Execution. Depending on decoding result, device control sends signals to the required
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parts of the processor: shaft, exchange unit with memory or changes the program counter. After execution, the result is saved in register or in memory. Program counter increases and the processor goes to next instruction. So step by step the same cycle repeats itself.
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The area of the crystal on which all these components are placed, limited. Because of this fundamental restrictions and two different ones arose approach to set design instructions. Cisco and risk. Cisk is complex set architecture instructions. Here every team can
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perform several actions at once. For example, one instruction can load a number from memory, add to him another and write down the result back. This approach is typical for X86 architecture used in most desktop computers. Risk - architecture with a simplified set
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instructions. Here the teams are at their maximum simple, and each one does one thing elementary action. Such instructions are executed very quickly, and complex ones operations are built from several simple ones.
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This approach is used, for example, in arm processors that are used in smartphones, tablets and microcontrollers.
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Cisco is betting on complexity universal commands. Less code, more difficult to decode. Risk on simplicity and speed. More code, faster execution. Despite the differences, both architectures serve one purpose: to allow the processor as quickly as possible and execute program commands more efficiently,
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stored in memory. To speed things up modern processors use work conveyor processing. Instead, to wait for one instruction the entire cycle will be completed, sampling decoding of execution. Conveyor allows the processor to do all these steps at the same time, but for different
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instructions. So far the first instruction is being executed, the second one is already being decoded, and the third one is selected from memory. It looks like this to the assembly line. Each stage the conveyor is constantly busy, that
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significantly increases the overall processor performance. Over time, engineers were faced with physical limit. Further increasing the speed at which it works the processor became inefficient due to problems with overheating and energy consumption.
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The idea of creating a multi-core processor appeared processor. The core is actually a full-fledged processor with its own ALU, UU and registers located on one crystal in one case with others the same nuclei. Instead of one processor worked very fast,
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multiple cores work in parallel. A multi-core processor can perform several tasks simultaneously, one for each core or split one big task into parts, that radically increases the overall performance.
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When executing a program, the processor have to turn to the same ones areas of relatively slow RAM. In order to don't waste time waiting, a small volume was created in the processor fast memory where the copy is stored
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data from RAM to which I often have to contact them. This memory is called the processor's cache memory.
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Cache memory is very fast and very dear memory, which is located directly on the processor crystal.
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It acts as a buffer that stores data and instructions to which the processor, most likely, contact the nearest time. The cache memory is divided into a hierarchy levels. The first level is the most Fastest and smallest cache memory.
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It's built right into each core. processor. Level 1 cache speed comparable to the speed of registers. Level second. It's bigger in volume, but a little bit slower than first-level memory.
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It is also usually tied to a specific core. On the third level is the largest and the slowest. Third level cache, as a rule, is common to all processor cores. Its purpose is to ensure fast communication between them and
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store a large array frequently data used. Thus, the processor is constantly searching for the necessary data according to a strict hierarchy. First in registers, then the first level, the second level and then the third level. And that's all
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If he doesn't find it anywhere, he is forced access slow operational memory. Such a complex memory hierarchy along with multi-core, pipeline processing and two different approaches to architecture makes a modern processor the incredibly fast and complex computing center.
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As you get to know the processor, you may the question arises: what exactly do they look like?
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instructions that the processor executes? What exactly does the processor read from memory? All commands that execute processor, written in machine language code of long sequences of zeros and units. Each such combination has strictly defined meaning. For For clarity, let's look at a small fragment
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machine code. This is a thirty-two-bit instruction for processors of the ARM family. This the sequence is divided into key fields. The condition field occupies bits with thirty-first to twenty-eighth. IN unlike many other processors, ARM architecture has a unique
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peculiarity. Each instruction starts with a special four-bit field. Conditions. This field allows the processor to make a decision: execute the current command or skip her. The conditions depend on the status flags, which were established by previous operations, for example, after comparison
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two numbers. If the processor status matches the condition, command is being carried out. If not, the processor instantly skips the command and goes on to the next one. In our code 10 means all execute the instruction Always.
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The next field is the instruction type. This the field serves as a kind of main switch or filter. It determines which category refers to the team. Arithmetic, work with memory, transition. As a consequence, as interpret the remaining bits. In our
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In this example, code 001 tells the processor. This data processing team, and it uses immediate number.
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Thanks to this, the processor knows that bits 24 through 21 indicate the exact operation code. Bits with eleventh to zero means encoded numerical value operant, not a memory address or anything other. Operation code field bit twenty-four through twenty
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first. Upcд is an abbreviation for operation code. clearly defines which one must perform an elementary operation CPU. In our instructions 1101 means MOV operation, move data.
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Bit 20, known as S-bit or bit setting the state is simple a switch that allows you to precisely control the logic of the program. If Sbit is equal to one, the processor updates its status flags in accordance with
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result of the current operation. If S-bit is equal to zero, the command is executed, but The flags remain unchanged. In ours instructions Sbit is equal to zero, since a simple movement of a number should not change the state of flags. Registers bits with
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nineteenth to twelfth. Next The fields tell the processor where to get it from data and where to write the result, using ultra-fast internal memory processor. Registers. Bits with nineteenth to sixteenth. Register source. Specifies the register containing first operant. Beat fifteen to
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twelfth. Assignment register specifies the register to which it will be The result of the operation is recorded. In ours instructions source register RN ignored because we are moving a number, not the contents of a register. RD field points to register R7,
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bits eleven through zero. The last field contains directly the value to be moved. IN In this case, the number is four. Result.
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The instruction tells the processor move the number 4 to register R7. Write programs in machine code consisting of from just zero units, a person would be extremely difficult. That's why language exists assembler. It's a programming language, in which each expression represents
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itself is one machine language instruction. Assembly language operations consist of memocodes. readable abbreviations from English words that match processor obcode. Same instructions The ARM we just deciphered, can be represented by the following expression. It's much easier this way.
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Before you transmit the program, written in assembly language processor, it needs to be translated back to zeros ones. For this a special program is used Assembler. Although writing programs on assembly language is faster than machine code, it still takes
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a lot of time and specific to each architecture. To eliminate these disadvantages were developed high-level programming languages, which are syntactically closer to human language, but this is already completely another story.
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We have analyzed the work of two main components of a computing machine, memory and processor. However, to create a full-fledged computer to which we We're used to it, it's not enough.
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Both the processor and the RAM energy dependent. This means that when the power goes out they completely lose their contents.
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In other words, after turning on the power you need to download all the programs again RAM. Agree, no the most convenient solution. To eliminate this disadvantage, the computer is equipped with secondary data storage. In contrast from RAM, it
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energy-independent, that is, it saves data even when power outage. Most common types of secondary storage hard drives and solid state drives storage devices. Hard disk is classic device in which data is written and read from rotating magnetic plates using
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reading heads. Head moves over the surface of the plates, finding the desired sector and performing the recording or reading data, much like a needle on vinyl player. Process both mechanical and electromagnetic.
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Its advantages include a low price for gigabyte, high capacity, suitable for storage of archives, films, backups copies. Cons: relatively low speed due to mechanical moving parts parts, shock sensitivity, noise during work. Solid state the drive is a modern device,
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in which the data is stored in semiconductor memory cells, capable of storing an electric charge without power. Data read records occur entirely electronically in a way that has no moving parts, so operations are performed almost instantly.
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Its advantages: high operating speed speeds up the loading of operating systems and programs. noiselessness, resistance to vibrations and shocks, low energy consumption.
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Cons: Higher price per gigabyte, limited cell resource. However, in in modern models this is not significant for the average user. So, tough disk slow capacious cheap Suitable for long-term storage.
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The solid state drive is fast, compact, more expensive, ideal for operating system and programs, requiring instant access.
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If secondary storage is available the computer loads data from it when necessity. For example, when turning on computer operating system loaded from storage into RAM memory. When the user launches application, be it a text editor or a browser, its program code too
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is loaded from storage into memory. AND only after this the processor can start executing program commands.
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Secondary storage is a place for long-term permanent storage data, so it is simply called storage, while operational memory is just memory. Modern the computer must be able to interact with the user and the outside world. For this purpose it is used
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input/output device. They are divided by their functions. Input device allow the user to transmit information to the computer. Mouse, keyboard, microphone. The output device allows transmit information to the computer to the user. Monitor, speakers, printer. It is interesting that even the secondary
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storage is also considered a device input/output relative to the processor. For the processor it's just another a device from which one can read data or write it back. For data exchange between all major computer components used tire. Tires may have different options
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implementations, but in a general sense it is a set of conductors through which signals are transmitted. Via the processor bus receives instructions from memory, writes the results of calculations there, and also exchanges data with external devices. There are three main types
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types of tires, each of which is responsible for their part of the work. The data bus transmits the data itself between the processor, memory and input/output devices. Her The bit depth determines how much bits of information can be transmitted in
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one beat. The address bus transmits addresses memory cells or device ports, water outlets that he wants to contact CPU. It defines the maximum the amount of memory that the processor is capable of address. The control bus transmits signals that control the transmission process.
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For example, when to start and when to finish exchange. All three tires are working.
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in a coordinated manner, ensuring data exchange between all components of the computer. Together they form the system bus, the basis of processor-memory interaction and input/output devices.
Topics:IT basicscomputer sciencebinary codeMorse codeBraillelogic gatesbits and bytescomputer memoryelectrical circuitsinstruction sets
