Original code complement

Complement code Is a kind of use Binary system A method of representing signed numbers , It's also a way to change the sign of a number , Often in Computer science Use in . The complement is defined as a binary number of signed bits .

The biggest advantage of complement system is that it can be used in addition or subtraction , There is no need to use different calculation methods because of the positive and negative of the number . Only one addition circuit can handle all kinds of signed addition , And subtraction can be represented by the complement of one number plus another , Therefore, as long as there is an addition circuit and a complement circuit, all kinds of signed addition and subtraction can be completed , It's quite convenient in circuit design .

Why complement 0 There is only one ？

The relationship between complement and original code ： Complement code = The original code is reversed except for the sign bit +1（ The complement symbol bit can participate in the operation ）

Integers （0000 0000） Take the opposite ：0111 1111 Add 1:0000 0000

     （1000 0000） Take the opposite ：1111 1111 Add 1:0000 0000（ Carry on 1 Be abandoned , Just don't take values anymore ）

Floating point numbers （0.0000） Take the opposite ：0.1111 Add 1:0.0000

       （1.0000） Take the opposite ：1.1111 Add 1：0.0000

Why can an eight digit integer complement represent -128, Floating point numbers can represent -1？

-127-1=1000 0001-0000 0001=1000 0000

or -127-1=1000 0001+1111 1111=1000 0000（ Carry away ）

Because of the complement +0 and -0 Use the same number to represent , So leave a number to represent -128

Floating point numbers are the same