Study notes: original code, inverse code, complement code

As a programmer , Always adhere to a belief , That's it Save farts and blow the lamp , This is also the source of everything .

1. CPU Adding is the fastest .
2. Try to convert subtraction operation into addition for calculation .
3. When binary represents numeric value , The highest is the sign bit , If you need to judge the symbol before calculating , It's complicated . Ideas , Let the symbols participate in the calculation （ Like normal addition ）

Original code

1. With 8 position Binary to represent a Numbers For example . The leftmost number 1 position As Sign bit , After the rest 7 position It can be used to express value .
   1.1. Positive numbers Symbol bit ：0： Such as ： 1 The binary of is 00000001
   1.2. negative Symbol bit ：1： Such as ：-1 The binary of is 10000001
2. Positive numbers Of Original code = Inverse code = Complement code . So we're talking about Inverse code , Complement code It mainly means negative .
3. The reason why we invented Inverse code , Complement code Just to make negative Binary operation of , and Positive numbers Keep the same operation rules （ Give Way Sign bit Participate in the calculation and will Subtraction Turn into Add Conduct ）, Finally, we can get the right result we want .

Inverse code

1. Positive numbers ： emphasize I've already said that Positive numbers Of Original code 、 Inverse code 、 Complement code Are all the same .
2. negative ： Sign bit unchanged , rest Each bit Take the opposite .
   2.1. -1 Original code ：1000 0001
   2.2. -1 Complement code ：1111 1110 （ Put it in 256 This value is 254 leave Complement number Still bad 1 ）
3. Use Inverse code Let Sign bit Also participated in the calculation , But there are still two problems ：
   3.1. We get less results than the real results 1.
   3.2. Save an embarrassing negative 0 problem ：1000 0000

Complement code

1. Positive numbers ： Again I've already said that Positive numbers Of Original code 、 Inverse code 、 Complement code Are all the same .
2. negative ： stay Inverse code On the basis of +1. Add the less inverse code operation 1, And make Plus or minus 0 The complement of is the same , It's solved -0 problem .
   -0 Original code ：1000 0000
   -0 Inverse code ：1111 1111 （ This value is parsed as the original code 255 ）
   -0 Complement code ：0000 0000 be equal to +0 = 0000 0000 （ Sign bit overflow , Back to a positive number )
3. Artificial definition 1000 0000 by -128, So that what we see Value range Negative numbers will be one more than positive numbers ：[-128, 127]

principle

With The clock For example , The current hour hand points to 6 spot , If you want to adjust it to 3 spot , There can be two options ：

1. Adjust clockwise ：+9 namely 6+9=3.
2. Counterclockwise adjustment ：-3 namely 6-3=3. To equivalent addition ：6+(12-3)

Success will subtract -3 Replace with +9 The result is the same . Because they are in the same 12 In the closed loop , Complement each other .
our Complement code It's the same thing . 0000 0000 this 8 position Binary number is a 256 Big ring .（ The maximum value is 255 add 1 To 256 It's the next round 0 了 , Just like there is no tonight 24 spot , Only tomorrow 0 spot ）

example ： stay 256 In the circle of , backward -1 Equal to forward +255.
（+255 yes -1 With 256 For the mold Complement number ）
-1 Original code ：1000 0001
-1 Inverse code ：1111 1110 （ Put it in 256 This value is 254 Complementary number 255 Still bad 1 ）
-1 Complement code ：1111 1111. stay Inverse code above +1 Just right +255.

Conclusion ： subtract a number , be equal to add This is the number Complement code . because Complement code Convenience of calculation , So what is actually stored in the computer is Complement code .

Reference material

Zhang Ziqiu's blog ： Original code , Inverse code , Complement code Detailed explanation