Number system: counting according to the principle of carry is called the carry technology system.
Different number systems have different bases and positions.
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Base
Concept: The number of digits in each number system is called the base of the number system.
Number system Base Digital Binary 2 0 1 Octal 8 0 1 2 3 4 5 6 7 Decimal 10 0 1 2 3 4 5 6 7 8 9 Hexadecimal 16 0 1 2 3 4 5 6 7 8 9 A B C D E F
Every 2 into 1
Every 8 enters 1
Every 10 enters 1
Every 16 enters 1
Position power
Concept: In each number system, the position of a number is different, and the value represented by it is different, which is called different position weight.
For example: In binary 1111.11, the leftmost 1 represents 1*2^3=16, and the rightmost 1 represents 1*2^-2=0.25.
Octal 2222.22 2 2*8^3 2*8^-2
Decimal 3333.33 3 3*10^3 3*10^-2
Hexadecimal 4444.44 4 4*16^3 4*16^-2
Writing rules
Written rules
Method 1: Add English letters after the number
B (binary) represents a binary number , and binary 101 can be written as 101B .
O (octonary) represents an octal number , and octal 101 can be written as 101O or 101Q .
D (decimal) represents a decimal number , and decimal 101 can be written as 101D .
H (hexadecimal) represents a hexadecimal number , and hexadecimal 101 can be written as 101H .
Method 2: Add a number subscript outside the brackets
Programming rules
Binary integer, requires 0b or 0B beginning, such as: 0b11
Decimal integer, such as: 99, -500, 0
An octal integer, which must start with 0 , such as: 015
Hexadecimal number, requires 0x or 0X to start, such as: 0x15
Base conversion
Low to high
Summation
1. Binary -> Decimal
For example: 1 0 1 1 0 0 1. 1 0 1 1 1 B
=1*2^6+0+1*2^4+1*2^3+0+0+1*2^0+1*2^-1+0+1*2^-3+1*2^-4+1*2^-5
= 64 +0+ 16 + 8 +0+0+ 1 + 0.5 +0+ 0.125+0.0625+0.03125
= 89.71875D
2. Binary -> octal (take the three -in-one -> expand their sums right position)
With the decimal point as the boundary, divide it into three groups of one digit to the left and right , and fill in the zeros if the three digits are not enough. After grouping, the corresponding octal numbers are formed.
For example: 1 011 001. 101 11 B
=001 011 001 . 101 110 B
= 1 3 1 . 5 6 Q
3. Binary -> Hex (take the four -in-one -> expand their sums right position)
With the decimal point as the boundary, divide it into four groups of one digit to the left and right , and fill in the zeros if the four digits are not enough. After the group is divided, it corresponds to a hexadecimal number.
For example: 101 1001. 1011 1 B
= 0101 1001 . 1011 1000 B
= 5 9 . B 8 H
4. Octal -> Decimal
For example: 1 6 Q
=1*8^1+6*8^0
= 8 + 6
=14D
5. Octal -> Hexadecimal
Method: Octal -> Decimal -> Hexadecimal
High to low
Divide by two backward remainder method
1. Decimal -> Binary
The integer part is divided by 2 and the remainder is reversed , and the decimal part is multiplied by 2 and is rounded forward .
For example: 89.71875D=1011001.10111B
2. Octal -> Binary
Method 1: Each bit of the octal system is divided by 2 to take the remainder , each corresponding to three binary digits, and zeros are added to the leftmost when insufficient .
For example: 276.15Q=10 111 110.001 101B
Method 2: Expand each octal number into three binary digits ( take one into three ).
For example: 2 7 6. 1 5 Q
=010 111 110 . 001 101 B
3. Hexadecimal -> Binary
Method 1: Divide each bit of hexadecimal by 2 and take the remainder . Each corresponds to four binary digits. When insufficient, zero is added to the left .
For example: 3AC.1EH=11 1010 1100.0001 1110 B
Method 2: Expand each hexadecimal number into four binary digits ( take one into four ).
For example: 3 A C. 1 E H
=0011 1010 1100 . 0001 1110 B
4. Decimal -> Octal
Divide the integer part by 8 and take the remainder .
For example: 14D=16Q
