Binary Subtraction

0 – 0 = 0

1 – 0 = 1

0 – 1 = 1

  Digit “0” will transform to digit “1”,while 1 is borrow from the left side.

One’s Complement Addition and Subtraction

  N-bit represent integers in the range –(2^N-1-1) to +(2^N-1-1) or call modulo (2^N-1-1)

Example of Number Presentation :

The table show that all possible value is in 4-bit system:

No.	Positive binary (+)	Negative binary(-)
0	0000	1111
1	0001	1110
2	0010	1101
3	0011	1100
4	0100	1011
5	0101	1010
6	0110	1001
7	0111	1000
8	1111	0000

Two’s Complement Addition and Subtraction

  N-bit be defined as complement with respect to 2^N

  Equivalent taking one’s complement and then plus “1”

  N-bit can represent in the range –(2^N-1) to +(2^N-1-1)

Example :

Signal overflow :

  Different for unsigned and two’s complement representation.

  Not necessarily occur when it carry out of sign, but occur when the result is of the opposite sign.

  Two example of 8-bit for present the result of two’s complement addition.

-lee Man