-16 bits of the original inverse code complement of 128

What are the original, inverse, and complement of -128?

128 doesn’t have an original, inverse, or complement, but the complement is -128 to +127, so -128’s complement should be 10000000, and -128 doesn’t have an inverse. The original code of -128 = 1000000.

Everything else overflows, and in an 8-bit integer the original code takes values from -127 to +127 the inverse code as well.

Extended information:

All numbers in a computer are represented by a 0, 1 code, and the plus and minus signs of a number are no exception. If a machine number is n digits long, it is agreed that the leftmost bit is used as the sign bit, and the remaining n-1 bits are used to represent the value.

In the sign bit, “0” indicates a positive number; “1” indicates a negative number. The numeric bits represent the absolute value of the true value. Where less than n-1 bits, decimal in the lowest bit to the right of zero; integer in the highest bit to the left of zero to make up the n-1 bits. This form of computer coding is called primitive code.

Inverse code representation: the inverse of a positive number is the same as its original code; the inverse of a negative number is the inverse of its original code bit by bit, except for the sign bit.

In computer systems, values are always expressed and stored in complementary code. The reason is that, using the complement, the sign bit and the numerical domain can be treated uniformly; at the same time, addition and subtraction can also be treated uniformly. In addition, the complementary code and the original code are converted to each other, and the arithmetic process is the same, so no additional hardware circuitry is needed.

Baidu Encyclopedia – Original Code

Baidu Encyclopedia – Inverse Code

Baidu Encyclopedia – Complementary Code

What is the original code for the inverse of -128?

-128 doesn’t have an original or inverse code in eight-bit binary, only a complement.

And, in computers, there is only the complement, not the original and the inverse.

The point of using the complement is: [to convert subtraction to addition].

This enables the simplification of computer hardware.

The number of bits in a computer is fixed, which provides for the use of complementary codes.


For example, to qualify, with only two bits of decimal 0 to 99, the period is 100.

Subtracting one then , can then be replaced by +99:



Just keeping two digits and ignoring rounding, the result is the same.

99, then, is called the [complement] of -1.

The formula for the complement of a negative number: 100 + the negative number.


Computers use binary, which is usually specified as eight bits.

That is, 00000000 to 11111111 can be used, of which there are 256.

The corresponding decimal, is 0 to 255. the period is 256.

Subtracting one, then, can be replaced by +255.

That is:

The complement of -1 is 11111111 (decimal 255).

The complement of -2 is 11111110 (decimal 254).

The complement of -3 is 11111101 (decimal 253).

…. Minus one in order until -128….

The complement of -128, 10000000 (=128).

…. There are 128 negative numbers and their complements….


The formula for finding the complement of a negative number: [256 + that negative number].

Positive numbers: directly, without any conversion.


The complement is useful.

Original inverses, on the other hand, are useless.

So, in computers, there is no original or inverse code.

And besides, -128 doesn’t have an eight-bit primitive and inverse code!

Original and inverse codes, what are they, don’t have to care!