Why are binary, octal and hexadecimal systems used in computers?

Binary numbers. Writing is long, error-prone, and hard to remember, while the decimal system.

The conversion process between numbers and binary numbers is complicated, so hexadecimal numbers or octal numbers are generally used.

Number as an abbreviation for binary number.

Carry counting system.

The method of counting according to the principle of carry is called the carry counting system.

In the number system of carry counting is employed.

, if a numeric value is represented by r basic symbols (e.g., 0,1,2, ,r-1), it is called the radix-r number system, and r becomes the base of the number system. For example, the decimal number commonly used in daily life is r=10, that is, the basic symbols are 0, 1, 2, , 9.

If r=2, that is, the basic symbol is 0, 1 is a binary number.

For different number systems, their common features are:

1) Each number system has a fixed set of symbols: for example, the decimal number system has ten symbols: 0, 1, 2, , 9, and the binary number system, which has two symbols: 0 and 1.

2) Secondly, they all use position notation: that is, the values represented by the number symbols in different positions are different, which is related to the weight of their position.

For example, the decimal system can be expressed as:

It can be seen that the value of the weight in the various carry counting systems is exactly a certain power of the cardinality. Thus, the sum of the polynomials by its weights can be written for any number represented by the carry counting system, and any r-based number n can be expressed as:

The di in the formula is the basic number symbol used in the number system, ri is the bit weight (weight), and r is the cardinality, which represents different base numbers; m is the number of digits in the integer part and k is the number of digits in the decimal part.

Bit rights"with"Cardinality"are the two elements of the carry counting system.

In the decimal counting system, it is based on"Every 10 into 1"The principle of counting. In general, in the carry counting system with the base number r, it is based on"Every R into one"or"Feng Ji Jinyi"The principle of counting.

In microcomputers, binary, octal, and hexadecimal are commonly used. Among them, binary is the most widely used.

Table 2 shows several carry systems commonly used in computers.

The internal information transmission in the computer is binary, because there are only 2 kinds of general situations: yes and no, so they are replaced by 1 and 0 respectively, which is conducive to the judgment of the iron knot, because the binary number is too troublesome to write, so it is later written in 8 base and 16 base respectively (exactly the third and fourth power of 2, which is convenient for conversion), and the actual internal data transmission of the computer is binary.

Also, the 2 numbers in binary are: 0 and 1, not 1 and 2

The main reason why binary is used inside computers is that binary has the following advantages:

Technically easy to implement. It's easy to represent the binary digits 0 and 1 with a bistable circuit. Computers use binary for encoding, not the decimal system we are familiar with, and the most important reason is that binary is physically easier to implement.

Because electronic devices mostly have two steady states. For example, the conduction and cut-off of transistors, the high and low voltage, the presence and absence of magnetism, etc. And it is difficult to find an electronic device with ten steady states.

Using binary also has the advantage of being simple to operate. There are 55 rules for summing and quadrating in decimal and only 3 in binary, which simplifies the design of physical devices such as combinators. In addition, the computer has few parts, which can enhance the stability of the entire system.

Therefore, binary is a natural choice for computers.

High reliability. Only two digits 0 and 1 are used in binary, which is not prone to errors in transmission and processing, so it can be used to ensure that the computer has a high degree of reliability.

The rules are simple. Compared to decimal numbers, the rules of operation of binary numbers are much simpler, which not only simplifies the structure of the combinator, but also helps to increase the speed of operation.

Coincides with logical quantities. The binary numbers 0 and 1 correspond exactly to the logical quantities "true" and "false", so it is natural to use binary numbers to represent binary logic.

The conversion between binary and decimal numbers is fairly easy. When people use the computer, they can still use the decimal number nanometer that they are accustomed to, and the computer automatically converts it into a binary number for storage and processing, and automatically converts the binary number into a decimal number when the processing result is output, which brings great convenience to the work.

Binary is used because:

1. The technical implementation is simple, the computer is composed of logic circuits, and the logic circuits usually have only two states, the switch is turned on and off, and these two states can be represented by "1" and "0".

2. Simplified operation rules: There are three combinations of two binary numbers and product operations, and the operation rules are simple, which is conducive to simplifying the internal structure of the computer and improving the operation speed.

3. Suitable for logical operations: Logical algebra is the theoretical basis for logical operations, and binary has only two numbers, which coincides with the "true" and "false" in logical algebra.

4. It is easy to convert, and binary and decimal numbers are easy to convert to each other.

5. The binary representation of data has the advantages of strong anti-interference ability and high reliability. Because each bit of data has only two states, high and low, it can still be reliably distinguished whether it is high or low when there is a certain degree of interference.

In hexadecimal system, two-digit hexadecimal means exactly one byte, which is more convenient than decimal system.

To put it bluntly, the computer knows a bunch of circuits, and the only forms that the circuit can show are energizing and breaking, which is what we often say, on and off. It's not that the base system determines the basic way the computer operates, but that the binary system is just the base system that the computer can match to perfectly interpret this way of working.

Therefore, the base system executed in the computer foundation is what we call binary. Binary is also the base system that we need to know before learning to calculate.

Binary is the simplest, with only two states, 0 and 1, and the decimal system is too complex and more difficult for the machine to implement.

This is due to the cost reduction that allows the digital to be used through digital tubes, seven-segment displays, and calculators for the operator's console.

Octadecimal is widely used in computer systems such as PDP-8, ICL 1900 and IBM mainframes using 12-bit, 24-bit or 36-bit. Octadecimals are the basis for these, because their ideal binary abbreviation size is divisible by 3 (each octal number represents three binary digits).

Four, eight to twelve digits can concisely display the entire machine, and also reduce the cost so that the numbers are allowed to be used by digital tubes, seven-segment displays, and calculators for the operator's console, which is too complex to use in binary displays, whereas decimal displays require complex hardware, and hexadecimal displays require more digits.

Binary is binary, abbreviated as b.

Octal is octal, abbreviated as o.

The decimal system is decimal, and the abbreviation is prepared with d.

Hexadecimal is hexadecimal, abbreviated as h.

Features of binary numbers:

It consists of two basic characters, 0,1, and the law of binary number operation seems to be a joke every two into one.

In order to distinguish it from other decimal numbers, binary numbers are usually written with a base number 2 at the bottom right of the number, or a b after the addition of a number.

1) There are only two characters 0 and 1 in the binary number, indicating a component with two different steady states.

2) Binary number operation is simple, which greatly simplifies the structure of the arithmetic parts in the calculation.

Binary is a system of numbers that is widely used in computing technology. Binary data is a number represented by two numbers, 0 and 1, its base is 2, and the carry rule is to give one every two rounds.

Binary is a system of numbers that is widely used in computing technology. Binary numbers are numbers that are represented by two numbers, 0 and 1. Its cardinal number is 2, the carry rule is every two into one, and the borrowing rule is borrowing one as two, which was discovered by Leibniz, a German master of mathematical philosophy in the 18th century.

Current computer systems use basically binary systems, and data is stored in the form of complements in computers. Binary in a computer is a very tiny switch, which is on for 1 and off for 0.

The invention and application of the computer, which is known as one of the important symbols of the third scientific and technological revolution in the 20th century, because digital computers can only recognize and process strings of symbols. The mode of operation is binary. The 19th-century Irish logician George Bull's thought process of logical propositions was transformed into a kind of algebraic calculus of symbols, where binary is a base system in which the base is the basic operator.

Because it uses only two number symbols, it is very simple and convenient and easy to implement electronically.

Binary is every two into one.

Usually the stove shouts that our arithmetic is decimal, and 0-9 will go to 10 after passing, so from one to one, so that there is a second place, and the first one is counted from 0. Every 10 digits go up to one digit. This is the decimal system.

Binary is less than 10, and 2 is rounded.

For example, 1 is a beam argument ruler, what if you add 1? One plus will be 2, so it will go one place, and the first digit will be 0. And it is.

The oak height is the maximum number of digits only to 1, and the greater than 1 is to advance one place.

Other bases and so on.