This article describes the original code, anti-code and complement the concept, followed by introduction of several positive and negative conversion of the original code, anti-code and complement.
Machine number and the true value
Machine number
A number of binary representation. Wherein the binary bit represents the most negative, 1 for negative, 0 is a positive number. such as
5 (decimal) -> 00000101 (binary)
5 (decimal) -> 10,000,101 (binary)
True value
"+" Or "-" sign to indicate the size plus the absolute value of the value, the value represented by this form. The following example, + 5, -5.
5 (decimal) -> 00000101 (binary) -> + 5 + 000 = 0101
5 (decimal) -> 10000101 (binary) -> -0000101 = -5
To summarize, with the true value is the value of the sign, with the machine number 0 or 1 to indicate the sign of the value.
The concept of the original code, anti-code and complement
Let me talk about the conclusion:
- Positive original code, the inverted, complementary codes are the same;
- Negative original code: the most significant bit is 1, the remaining bits of the absolute value of the true value;
- Inverted negative: on the basis of the original code, change the sign bit, the remaining bits of bitwise;
- Negative complement: on the basis of the original code, change the sign bit, the remaining bits inverted, and finally add 1; that is added on the basis of the inverted one.
Original code
Original code: The first symbol representing the remaining bits represent value. for example
+ 12-> 0000 1100 (original code)
-12-> 1000 1100 (original code)
Is in the range corresponding to [1111 1111,0111 1111]the range [-127,127]
Inverted
Positive original code, the inverted, complementary codes are the same;
Inverted negative: on the basis of the original code, change the sign bit, the remaining bits of bitwise. for example:
+ 12-> 0000 1100 (original code) -> 0000 1100 (inverted)
-12-> 1000 1100 (original code) -> 11110011 (inverted)
Complement
Positive original code, the inverted, complementary codes are the same;
Negative complement: for example 12,
- -12 original code: 10001100
- MSB unchanged, and the remaining bit is inverted: 11,110,011
- Was added to obtain a complement: 11110100
Here if you want to turn negative complement the original code, the same method of operation;
- -12 Complement: 11,110,100
- MSB unchanged, and the remaining bit is inverted: 10,001,011
- Was added to give a primitive: 10001100
About complement the range Why is [-128 to 127] problem?
The question I did not get to know, you can look at the second reference links, think about.
Reference links