Binary, octal, decimal, hexadecimal number conversion method - Database & Sql Blog Articles

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A), binary system is used in binary, because binary has simple operation, easy to implement and reliable, provides a favorable way for logic design, saves equipment and other advantages, for the convenience of description, commonly used as eight, hexadecimal Abbreviation for binary.
The general count uses the carry count, which is characterized by:
(1) Every time N is entered, N is the base number of each carry count system indicating the number of symbols required for a single digit.
(2) With position notation, the values ​​represented by the numbers at different positions are different, and the value represented by the unit number at the fixed position is determined, and the value at this fixed position is called the weight.
In the computer: D7 D6 D5 D4 D3 D2 D1 D0 only two 0 and 1
8 4 2 1
2) Conversion principle between the number system conversion and different carry count systems: The conversion between different carry count systems is based on the principle that the two rational numbers are equal, and the two integers and the fractional parts must be equal. In other words, if the two numbers before the conversion are equal, they must still be equal after the conversion.
There are hexadecimal decimals: there are 10 bases: 0 ~~ 9 , every ten decimals and one binary: there are 2 bases: 0 ~~ 1 , every two in one octal: there are 8 bases: 0 ~~ 7 , every eight Into a hexadecimal: there are 16 bases: 0 ~ ~ 9, A, B, C, D, E, F (A = 10, B = 11, C = 12, D = 13, E = 14, F =15), every sixteen into one
1, the number of carry count
N=a n-1*p n-1+a n-2*p n-2+...+a2*p2+a1*p1+a0*p0
2, the conversion between decimal and P-ary numbers 1 decimal conversion to binary: decimal integer conversion to binary integer is usually divided by 2 remainder method, fractional part multiplied by 2 rounding method. For example, convert (30) 10 to a binary number.
Convert (30)10 to binary number
2| 30 ....0 ---- the rightmost position
2 15 ....1
2 7 ....1
2 3 ....1
1 ....1 ---- leftmost position ∴ (30) 10=(11110)2
Convert (30)10 to eight, hexadecimal
8| 30 ......6 ------most right position
3 ------leftmost position ∴ (30) 10 = (36) 8
16| 30 ... 14(E)----The rightmost position
1 ---- leftmost position ∴ (30) 10 = (1E) 16
3. Convert the P-ary number to a decimal number Convert a binary to decimal. Use the method: multiply the last digit of the binary by 20, the second-to-last digit by 21, ..., and multiply the highest digit by 2n. The result of adding the products is then its decimal expression.
Convert binary 11110 to decimal (11110) 2=1*24+1*23+1*22+1*21+0*20=
=16+8+4+2+0
=(30)10
Convert an octal to decimal method: multiply the last digit of the octal by 80, multiply the second digit by 81, ..., multiply the highest digit by 8n, and then add the products to it. The decimal expression.
Convert octal 36 to decimal (36) 8=3*81+6*80=24+6=(30)10
Convert a hexadecimal to decimal method: multiply the last digit of the hexadecimal by 160, multiply the second to last digit by 161, ..., multiply the highest digit by 16n, and then multiply the products. The result of the addition is its decimal expression.
Convert 16+ 1E to decimal (1E)16=1*161+14*160=16+14=(30)10
3, binary conversion to octal number
(1) Convert binary numbers into octal numbers: For integers, divide every three digits of the binary number from low to high. If there are not enough three digits, add 0 to the left of the high digit, make up three digits, and then each three digits. Binary numbers are replaced with an octal number, starting from the decimal point and converting from left to right every three digits. E.g:
Convert binary number 1101001 to octal number, then
(001 101 001) 2
| | |
( 1 5 1)8
(1101001) 2 = (151) 8
(2) Convert octal numbers into binary numbers: just replace each octal number with a three-digit binary number to complete the conversion. For example, if you convert an octal number (643.503) 8 into a binary number,
(6 4 3 . 5 0 3)8
| | | | | |
(110 100 011 . 101 000 011) 2
(643.503) 8=(110100011.101000011)2
4, the conversion between binary and hexadecimal
(1) Converting a binary number to a hexadecimal number: Since the 4th power of 2 = 16, in accordance with the binary and octal conversion methods, each four digits of the binary number is represented by a hexadecimal number, the integer part The decimal point is converted from right to left every four-digit group, and the decimal part is converted from left to right every four-digit group starting from the decimal point.
(2) Converting hexadecimal to binary numbers If you convert a hexadecimal number into a binary number, you can complete the conversion by expressing each hexadecimal number with four corresponding binary numbers.
For example: convert (163.5B) 16 to a binary number, then
( 1 6 3 . 5 B )16
| | | | |
(0001 0110 0011. 0101 1011 ) 2
(163.5B)16=(101100011.01011011)2
The easiest way to convert from binary to decimal? ?
Such as: (10111) 2
=((((0*2+1)*2+0)*2+1)*2+1)*2+1)10
=(((1*2+0)*2+1)*2+1)*2+1)10
=((((2+0)*2+1)*2+1)*2+1)10
=(((2*2+1)*2+1)*2+1)10
=(((4+1)*2+1)*2+1)10
=((5*2+1)*2+1)10
=((10+1)*2+1)10
=(11*2+1)10
=(22+1)10
=(23)10