Original code, inverse code, complement code

End the conversion of various hexadecimals , Let's talk about another topic ： Original code 、 Inverse code 、 Complement code .

We already know that computers , All data is ultimately expressed in binary numbers .

We have also learned how to make a 10 How to convert a base number to a binary number .

however , We still haven't learned how to express a negative number in binary .

such as , Suppose there is a int Number of types , The value is 5, that , We know that it's represented in a computer as ：

00000000 00000000 00000000 00000101

5 The conversion to two systems is 101, however int Type of number occupied 4 byte （32 position ）, So there's a pile of 0.

Now I want to know ,-5 How to express in a computer ？

In the computer , A negative number is expressed as a complement to its positive value .

What is complement ？ This has to come from the original , The irony is that .

Original code ： An integer , Binary number converted by absolute value size , It's called the original code .

such as 00000000 00000000 00000000 00000101 yes 5 Of Original code .

Inverse code ： Invert binary numbers bit by bit , The resulting new binary number is called the inverse of the original binary number .

Reverse operation means ： originally 1, have to 0; originally 0, have to 1.（1 change 0; 0 change 1）

such as ： take 00000000 00000000 00000000 00000101 Reverse each bit , have to 11111111 11111111 11111111 11111010.

call ：11111111 11111111 11111111 11111010 yes 00000000 00000000 00000000 00000101 The inverse of .

The irony is mutual , So it can also be called ：

11111111 11111111 11111111 11111010 and 00000000 00000000 00000000 00000101 It's the opposite of each other .

Complement code ： Counter code plus 1 It's called complement .

in other words , To get a complement of numbers , First get the inverse , Then add the inverse to 1, The resulting number is called complement .

such as ：00000000 00000000 00000000 00000101 The opposite of ：11111111 11111111 11111111 11111010.

that , The complement is ：

11111111 11111111 11111111 11111010 + 1 = 11111111 11111111 11111111 11111011

therefore ,-5 It's expressed in a computer as ：11111111 11111111 11111111 11111011. Convert to hex ：0xFFFFFFFB.

Take another example , Let's look at integers -1 How to express in a computer .

Suppose this is also a int type , that ：

1、 First 1 The original code of ：00000000 00000000 00000000 00000001

2、 We have to counter ： 11111111 11111111 11111111 11111110

3、 Get complement ： 11111111 11111111 11111111 11111111

so ,－1 In a computer, binary expression is all 1.16 Into the system for ：0xFFFFFF.