Computer Science – Data representation | e-Consult

Two's complement is used because it provides a simple and efficient way to perform arithmetic operations (addition and subtraction) on both positive and negative numbers using the same circuitry. It avoids the need for separate addition circuits for positive and negative numbers, as required by sign-magnitude.

Sign-magnitude representation uses one bit to represent the sign (0 for positive, 1 for negative) and the remaining bits to represent the magnitude of the number. This results in two representations of zero (positive and negative), and the addition/subtraction circuits are more complex. It is less efficient than two's complement.

Two's complement simplifies arithmetic by allowing addition and subtraction to be performed using the same logic circuits. The process of converting a negative number to two's complement is straightforward (inverting all bits and adding 1), and the sign bit is automatically handled during addition.

Comparison:

• Efficiency: Two's complement is more efficient for arithmetic.
• Zero Representation: Sign-magnitude has two representations of zero, while two's complement has only one.
• Complexity: Sign-magnitude has more complex addition/subtraction circuits.
• Range: Two's complement allows for a wider range of representable numbers for a given number of bits.