? In mathematics and digital circuits, binary refers to a numeration system based on 2, which means that this system is binary. In this system, 0 and 1 are usually used. In digital circuits, logic gates are directly binary. Therefore, modern computers and computer-dependent devices all use binary, and each number is called a bit (binary bit). Bit is the abbreviation of binary number, and this term was first formally used in Shannon's famous paper Mathematical Theory of Communication on page 1.
? A bit is a bit in the binary system and the smallest unit of information. Bits are mixed words of binary numbers.
? 1605, Francis Bacon proposed a system that can convert 26 letters into binary numbers. In addition, he added, this idea can be applied to anything: "as long as the differences between these things are simple opposites, such as bells and horns, lights and flashlights, and the shooting sound of rifles and similar weapons." This is of great significance to the general theory of binary coding. (See Bacon Password)
? The modern binary numeration system was designed by gottfried leibniz in 1679, and it appeared in his article "On binary arithmetic using only symbols 0 and 1, its use and the significance it gave Fuxi to use ancient graphics" [1]. Systems related to binary numbers also appeared in some earlier cultures, including ancient Egypt, China and India. China's Book of Changes especially aroused Leibniz's association.
? The full name of Leibniz's paper on binary system is "On binary arithmetic using only symbols 0 and 1, its use and the significance it gives Fuxi to use ancient graphics" (1703). Similar to the modern binary counting system, Leibniz's system uses 0 and 1. The following is an example of the Leibniz binary counting system:
? 1954, British mathematician george boole published a landmark paper, in which an algebraic logic system was introduced in detail, which was later called Boolean algebra. His logic calculus played a fundamental role in the later electronic circuit design.
? Here, we are going to learn Boolean algebra.
? Logical algebra is a branch of algebra, and its variable value only consists of true and false, in fact, it is 1 and 0. The main operation of logical algebra is NAND, so it is a formalism to describe logical relations by describing numerical relations with ordinary algebra. George boole introduced logic algebra in his first book, Mathematical Analysis of Logic (1847), and put forward logic algebra more comprehensively in Research on the Law of Thinking (1854). [[1]] (https://zh.wikipedia.org/wiki/logical algebra #cite_note- 1) was first proposed by Sheffer in 19 13 according to the word "Boolean algebra" in Huntington. [ 2]
? Variables involved in logical operations are called logical variables and are represented by letters a, b …. The value of each variable is not 0, that is, 1. 0 and 1 do not represent the size of numbers, but represent two different logical states.
Positive and negative logic stipulates:
The basic operations of logical algebra are as follows.
? At the beginning of the 20th century, some electronic engineers realized that logic algebra was very similar to some electronic circuits. Shannon proved that this behavior is equivalent to logical algebra in his paper 1937.
Almost all modern general-purpose computers use binary Boolean logic for operations. In other words, their circuits are physical representations of binary Boolean logic. Several representations: voltage on wires, direction of magnetic domains in magnetic storage devices, holes in punched cards or paper tapes, etc. (But some early computers used decimal circuits or machinery instead of binary logic circuits).
Of course, more than two symbols can also be encoded in any medium. For example, use 0,0 1, 2,3 volts on the conductor, encode a character set with four symbols, or use holes of different sizes on punched cards. But in fact, noise is the key factor of small high-speed and low-power circuits. This makes it difficult to distinguish between multiple possible symbols. So the circuit designer chose two kinds of voltages, high and low, instead of four.
For the above reasons, computers use binary logic circuits. The most common computer architecture uses 32 or 64 Boolean sequences called bits, such as 01110101/kloc-0. When using machine language, assembly language and some advanced languages, programmers can manipulate the digital structure of registers. In the register, voltage 0 represents logic 0, and the reference voltage (usually +5 volts or +3.3 volts [[4]] (https://zh.wikipedia.org/wiki/logic algebra #cite_note-4)) represents logic 1. These languages support numerical operations and logical operations. The "numerical operation" here refers to the operation of adding, subtracting, multiplying and dividing a bit sequence as a binary number by a computer. "Logical operation" refers to the AND or NOT operation between two bit sequences, and each bit in one sequence is operated with the corresponding bit in the other sequence. The key difference between these two operations is that the former has carry and the latter does not.
? From 65438 to 0937, claude shannon completed his master's degree thesis in electrical engineering at MIT, and realized Boolean algebra and binary arithmetic operations with relays and switches. The topic of this paper is "Symbolic analysis of relays and switching circuits" [7], in which Shannon's theory laid a theoretical foundation for digital circuits. Shannon won the 1940 American Engineer Award from Alfred Nobel Society for this paper. Howard gardner of Harvard University said that Shannon's master's thesis "may be the most important and famous master's thesis in this century".
? Have any readers seen the mystery of coding? The sixth chapter of this book has introduced what a relay is, but the exact name is electromagnetic relay. In the mystery of coding, it seems easy to know what a relay is, that is, an electrical appliance that connects one coil with another to continue working. But the explanation in wiki is not like this, and the author is also curious about how the name relay is translated. The explanation in the wiki is as follows: