Original code, inverse code and complement code

1. Original code

The original code is the absolute value of the sign bit plus the true value , That is to say, the symbol is represented by the first digit , The rest of the bits represent the value . For example, if it is 8 Bit binary :

[+1] primary  = 0000 0001

[-1] primary  = 1000 0001

The first bit is the sign bit . Because the first bit is the sign bit , therefore 8 The value range of bit binary number is :

[1111 1111 , 0111 1111]==>[-127 , 127]

2. Inverse code

The representation of the inverse code is :

• The inverse of a positive number is itself
• The inverse of a negative number is based on its original code , The sign bits remain the same , The rest of the bits are reversed .

[+1] = [00000001] primary  = [00000001] back 

[-1] = [10000001] primary  = [11111110] back 

3. Complement code

The representation of complement is :

• The complement of a positive number is itself
• The complement of a negative number is based on its original code , The sign bits remain the same , The rest of you take the opposite , Last +1. ( That is, on the basis of the inverse code +1)

[+1] = [00000001] primary  = [00000001] back  = [00000001] repair 

[-1] = [10000001] primary  = [11111110] back  = [11111111] repair 

The operation of complement ：
　　 One 、 Complement addition
　　[X+Y] repair = [X] repair + [Y] repair
　　 example ：X=+0110011,Y=-0101001, seek [X+Y] repair
　　[X] repair =00110011 [Y] repair =11010111
　　[X+Y] repair = [X] repair + [Y] repair = 00110011+11010111=00001010
　　 notes ： Because the bit length of the arithmetic unit in the computer is fixed , The highest carry generated in the above operation will be discarded , So the result is not 100001010, It is 00001010.
　　 Two 、 Complement subtraction
　　[X-Y] repair = [X] repair - [Y] repair = [X] repair + [-Y] repair
　　 among [-Y] Complement is called negative complement , The way to find the negative complement is ： All bits of the original code of the absolute value of a negative number are reversed bit by bit ; And then add the whole number 1.
　　 example ：1+（-1) [ Decimal system ]
　　1 The original code of 00000001 Convert to complement ：00000001
　　-1 The original code of 10000001 Convert to complement ：11111111
　　1+（-1)=0
　　00000001+11111111=00000000
　　00000000 Convert to decimal to 0
　　0=0 So the calculation is correct .
　　 3、 ... and 、 Complement multiplication
　　 Set the multiplicand 【X】 repair =X0.X1X2……Xn-1, The multiplier 【Y】 repair =Y0.Y1Y2……Yn-1,
　　【X*Y】 repair =【X】 repair ×【Y】 repair , Multiplier （ Multiplier ） The complement of multiplication is equal to the multiplication of complement .