Base conversion and the conversion of the original anti-code and complement

First, the binary conversion

　　1, and the number of system code system

 

Common number system representation

Decimal	Binary	Octal	Hex	8421BCD code
0	0	0	0	0000
1	1	1	1	0001
2	10	2	2	0010
3	11	3	3	0011
4	100	4	4	0100
5	101	5	5	0101
6	110	6	6	0110
7	111	7	7	0111
8	1000	10	8	1000
9	1001	11	9	1001
10	1010	12	A	0001 0000
11	1011	13	B	0001 0001
12	1100	14	C	0001 0010
13	1101	15	D	0001 0011
14	1110	16	E	0001 0100
15	1111	17	F	0001 0101

 

 

 

 

 

 

 

 

 

 

 

 

　　1, conversion between binary and decimal

　　　　Conversion principles: the right to expand by adding a binary number written in the form of a sum of the respective power of N, and decimal calculation result.

　　　　（10111101）₂ = 1x2⁷+0x2⁶+1x2⁵+1x2⁴+1x2³+1x2²+0x2¹+1x2⁰ = (189)₁₀

　　2. Binary octal

   　　   Binary ( . 1 110    110   111   011   100 ) ₂  = (166734) ₈

  　　    Octal 166 734

　　3, Binary Hex

　  Binary ( 1101    1001   1110   0100 ) ₂ = (D9E4) ₁₆

      Decimal 139144

      Hex D 9 E 4

4, Binary Code 8421bcd

　　Binary 8421bcd code can not be transferred directly, usually the first binary number to decimal number, and then converted to bcd code

　　（1101）₂ = （13）₁₀ = （0001 0011）_bcd

5, M-ary conversion into a decimal

　　Conversion principles: the right to expand by adding the M-ary number is written in the form of a sum of the respective power of N, and decimal calculation result.

　　（5213）₆ = 5 x 6³ + 2 x 6²+ 1 x 6¹+ 3 x 6⁰ = (1186)₁₀

6, the decimal conversion into N-ary

　　Conversion principles: N down after decimal addition modulo (150) ₁₀ = (226) ₈

　　

　　

Second, the original anti-code and complement

　　Binary numbers, the first bit is the sign bit, 1 for negative, 0 for positive

1, positive: anti-code and complement as the original code

2, negative:

　　　　Original code: most significant bit is 1, followed by the absolute value of the binary number

　　　　Inverted: the symbol bit constant data bit bitwise

　　　　Complement: In its last bit inverted +1

3, computing

　　在计算机中运算中，加减法是高频运算，使用同一个运算器，可以减少中间变量存储的开销，这样也降低了CPU内部的设计复杂度

　　减去一个数等于加上这个数的负数

　　两个正数正数相加时，按照二进制加法直接计算即可

　　如果有负数参与计算时则要使用其补码来参与计算。

　　例                 

             

　　　　　　　　　　负数：最左一位表示负，右面七位按位取反+1   -（0000010）=-2