Integer Representation (Fixed-point representation)

Sign magnitude representation:

There are several alternative convention used to represent negative as well as positive integers, all of which involves treating the most significant (left most) bit in the word as sign bit. If the sign bit is 0, the number is +ve and if the sign bit is 1, the number is –ve. In n bit word the right most n-1 bit hold the magnitude of integer.

For an example,

+18 = 00010010

- 18 = 10010010 (sign magnitude)

The general case can be expressed as follows:

2’s complement representation:

Like sign magnitude representation, 2’s complement representation uses the most significant bit as sign bit making it easy to test whether the integer is negative or positive. It differs from the use of sign magnitude representation in the way that the other bits are interpreted. For negation, take the Boolean complement (1’s complement) of each bit of corresponding positive number, and then add one to the resulting bit pattern viewed as unsigned integer. Consider n bit integer A in 2’s complement representation. If A is +ve then the sign bit a_n-1 is zero. The remaining bits represent the magnitude of the number.