Generic selectors
Exact matches only
Search in title
Search in content
Post Type Selectors

Explain signed magnitude, signed l’s complement and signed 2’s complement representation of numbers. Find the range of numbers in all three representations for 8 bit register.

Signed magnitude, signed 1’s complement, and signed 2’s complement are three methods of representing signed numbers in binary form.

Signed magnitude

Signed magnitude representation represents a signed number using the most significant bit as a sign bit (0 for positive numbers, 1 for negative numbers) and the remaining bits as the magnitude of the number. For example, in 8-bit signed magnitude representation, the number +7 is represented as 00000111 and the number -7 is represented as 10000111.

Signed 1’s complement

Signed 1’s complement representation represents a signed number by taking the 1’s complement of the magnitude of the number and then adding a sign bit. The sign bit is 0 for positive numbers and 1 for negative numbers. For example, in 8-bit signed 1’s complement representation, the number +7 is represented as 00000111 and the number -7 is represented as 11111000.

Signed 2’s complement

Signed 2’s complement representation represents a signed number by taking the 2’s complement of the magnitude of the number and then adding a sign bit. The sign bit is 0 for positive numbers and 1 for negative numbers. To compute the 2’s complement of a number, we invert all its bits and add 1 to the result. For example, in 8-bit signed 2’s complement representation, the number +7 is represented as 00000111 and the number -7 is represented as 11111001.

The range of numbers in all three representations for 8 bit register is as follows:

Signed magnitude: -127 to +127
Signed 1’s complement: -127 to +127
Signed 2’s complement: -128 to +127