What does the decimal system mean in a computer?

Notation of binary numbers.

Binary is a system of numbers that is widely used in computing technology. Binary numbers are numbers represented by two numbers, 0 and 1. Its base is 2, the carry rule is "every two into one", and the borrowing rule is "borrow one as two".

Binary numbers are also based on position notation, and their bit weights are based on 2 powers. For example, a binary number whose weights are in the order of -2. For integers with n digits, binary numbers with m decimal places are expressed by a weighted coefficient formula, which can be written as:

a(n-1)a(n-2)，a(-m)）2＝a(n-1)×2^(n-1)+a(n-2)×2^(n-2)+，a(1)×2^1+a(0)×2^0+a(-1)×2^(-1)+a(-2)×2^(-2)+a(-m)×2^(-m)

Binary numbers can generally be written as: (a(n-1)a(n-2). a(1)a(0).a(-1)a(-2)…a(-m)）2。

Note:1where aj denotes the coefficient of the j-th position, which is a number between 0 and 1.

(n-1) in is the subscript, the input method can not be typed, so enclosed in parentheses, to avoid confusion.

Represents the square of 2, and so on.

Example 1102] Write the binary number in the form of a weighted coefficient.

Solution: (The basic rules of arithmetic operations on binary numbers are very similar to those for decimal numbers.) The most commonly used are addition and multiplication.

These calculations are the same as addition or multiplication in decimal, except that the number of the decimal digits is different, and the decimal system is carried to ten, and here it is entered to 2).

Use the eight numbers 0, 1, 2, 3, 4, 5, 6, 7, every octal place, and the beginning must start with the number 0. Octal numbers are easier to write than binary numbers, and are often used in computer calculations.

For example, 32 in decimal 10 is represented as 40 in occimal

9 and 27 in decimal 10 are recorded as 11 and 33 in octal

The base 32 in base 8 is represented as a base of 10, which is: 3 8 1 + 2 8 0 = 26

It consists of 0-9, a-f, . The correspondence with decimal is:

0-9 corresponds to 0-9;

a-f corresponds to 10-15;

Numbers in base n can be represented by numbers ---n-1) in 0 and 9 with the letters a-f

For example, 32 in decimal 10 is represented as 20 in hexadecimal

32 in hexadecimal is represented as decimal, which is: 3 16 1 + 2 16 0 = 50

In layman's terms: binary is the base system used in computer calculations, and base 10 is used in daily calculations. The hexadecimal system is generally used by computers to set various serial numbers, passwords, and hard disk serial numbers.

That's probably what it means.

The representation of numbers, the numbers we usually talk about are in decimal system, such as the addition of two numbers is every decimal one.

Its representation is naturally within 10, such as 321; The number on the first bit is lower than 10;

In the same way, the binary representation must be within 2, such as 101010; It's every two into one;

The octal system can be represented by 0,1,2,3,4,5,6,7, and every eight into one;

Hexadecimal is special, it is represented by 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e, f, every 16 to 1!

They can be converted between them, e.g. decimal 15 can be expressed in the following form:

Binary: 1111

Oct: 17

Hexadecimal: f

You need to check the information separately for the specific conversion method!

Basemal: There are only the numbers 0 and 1, that is, every 2 into 1

Baseling: It is the number 0 to 7, every 8 to one.

Decimal: It is the number 0 to 9, every 10 into one.

Hexadecimal: It is the number 0 to 9, plus the letters A to F, A to F represent 10 to 15, every 16 to one.

In our daily life, the decimal system is generally used. That is, after counting from 0 to 9, you have to advance a handful of numbers to become 2 digits, and the same is that the base system has to be advanced from 0 to 1 to become 2 digits. 8 is to advance one from 0 to 7, and 16 is to advance one from 0 to 15.

Only binary can be recognized in the computer. These bases are just a common algorithm.

Computers are in binary, not decimal.

The base systems of numbers commonly used in computers mainly include: binary, octal, and hexadecimal.

base 2 with two Arabic numerals;

base 8, with eight Arabic numerals; base 10 with ten Arabic numerals: 0 to 9;

The base hexadecimal system is every 16 into 1, but we only have the ten numbers 0 and 9, so we use the six letters a, b, c, d, e, and f to represent 10, 11, 12, 13, 14, and 15 respectively. Letters are not case sensitive.

Binary: Every two into one, indicating the number: 01.

The computer's decimal system is a carry counting system, which has only 10 numeric symbols 0 to 9. In computer science and electronic engineering, the use of decimal systems is common, especially for representing memory addresses and data.

Corresponding to this is the binary, octal, and hexadecimal carry counting system. The binary system has only two numeric symbols, 0 and 1, which are used for data storage and processing inside the computer. The octal and hexadecimal systems have been successively expanded into 8 and 16 number symbols, which are convenient for operation and representation in application scenarios such as writing and data transmission.

Although computers are inherently binary-based, there are situations where converting their data to decimal is more understandable and operational. For example, in the world of image processing, each pixel has its own RGB values (red, green, and blue primary colors), and these values are usually expressed in a decimal system.

The computer uses binary, through the binary calculation method, the desired result can be quickly calculated, and the computer can make the calculation speed faster through the binary method, and it is very easy to use.

Binary, that is, full two into one.

Hexadecimal: A counting system that uses 16 as the base number. The numbers 0-9 and the letters a-f (or their capitalized a-f) represent 0 to 15.

H is used for hexadecimal.

The base system commonly used in computers is binary, and the base system has binary, octal, decimal, and hexagram maloction. binary, with two Arabic numerals; octal, with eight Arabic numerals, envy and virtuality; decimal, with ten Arabic numerals: 0 to 9; The hexadecimal system is every 16 into 1, but there are only ten numbers 0 and 9, so the five letters a, b, c, d, e, and f are used to represent 10, 11, 12, 13, 14, and 15 respectively.

Letters are not case sensitive.

Putting each bit of the decimal system as a four-digit binary number is as simple as that, and it's easy to remember 8421 yards from 0-9. Example:

Decimal conversion to BCD code, integers start on the right, and each number is a 4-digit binary**.

For example: (195)10=(110010101)bcd, the decimal is not the same as other base conversions, it is a digital conversion: (

Computers are in binary, not decimal.

The decimal system is based on the principle of decimal and decimal places, that is, all numbers are represented by 10 basic symbols, full decimal one, and the same symbol represents different values in different positions, and the position of the symbols is very important.

Human arithmetic uses the decimal system, which may have something to do with the fact that humans have ten fingers. Aristotle claimed that the universal use of the decimal system is simply the result of the anatomical fact that the vast majority of people are born with 10 fingers.

"Decimal" in a computer means:

Base 2: There are only the numbers 0 and 1, that is, every 2 into one;

Baseling: It is the number of Fanming Hall 0 to 7, every 8 into one;

Decimal: It is the number 0 to 9, every 10 into one.

Hexadecimal: It is the number 0 to 9, plus the letters A to F, A to F represent 10 to 15, every 16 to one.

The base system, also known as the carry system, is a method of carrying that people prescribe. For any kind of decimal --- the decimal system, it means that the number in a certain position is calculated every one digit of x. Decimal is every 10, Hexadecimal is 10, Binary is 100, and so on, and the base X is every X round.

A decimal number 110, where the 1 in the hundred digit represents 1 10 2, i.e. 100, the 1 in the ten digit represents 1 10 1, i.e. 10, and the 0 in the single digit means 0 10 0, i.e. 0.

A binary number 110, where the high 1 represents a 2 2, i.e., 4, the low 1 represents a 2 1, i.e., 2, and the lowest 0 represents 0 2 0, i.e., 0.

A hexadecimal number 110, where the 1 in the high position represents 1 16 2, i.e., 256, the low 1 represents 1 16 1, i.e., 16, and the 0 in the lowest digit represents 0 16 0, i.e., 0.

It can be seen that in the number system, the size of the value expressed by the number is not only related to the size of the number itself, but also related to the position of the number.

The bit weight of a decimal number is a power of 10, the bit weight of a binary number is a power of 2, and the bit weight of a hexadecimal number is a power of 16. The digits are arranged from high to low, in a decreasing power.