Information Representation
Computer Arithmetic - Binary Subtraction


To perform a binary subtraction you first have to represent the number to be subtracted in its negative form. This is known as its two's complement.

The two's complement of a binary number is obtained by:

  1. Replacing all the 1's with 0's and the 0's with 1's. This is known as its one's complement.

  2. Adding 1 to this number by the rules of binary addition.

Now you have the two's complement.


Example:
The decimal subtraction 29 - 7 = 22 is the same as adding (29) + (-7) = 22

  1. Convert the number to be subtracted to its two's complement:

    00000111 (decimal 7)
    11111000 (one's complement)
    + 00000001 (add 1)
    11111001 (two's complement)

    11111001 now represents -7.

  2. Add

    29 00011101
    +- 7 11111001
    22 (1)00010110

    Note that the final carry 1 is ignored.