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Signed Magnitude Numbers

Discussion of signed magnitude involves the classification of the numbers in digital system as signed or unsigned.

Un-signed Numbers:

In un-signed number system all the bits directly correspond to the equivalent decimal number.

Examples:

100011 binary = 35 decimal

000011 binary = 3 decimal

Signed Numbers:

In signed number system the most significant bit (msb) bit signifies sign of all lower significant bit (lsb) bits for the number. 

Examples:

100011 binary = -3 decimal

000011 binary = +3 decimal

In Digital Systems the negative numbers can be represented by following three ways:-

-3 in signed magnitude value               10011

-3 in signed 1’s complement value      11100

-3 in signed 2’s complement value      11101

Signed magnitude Addition Examples

Example:- Signed Magnitude Arithmetic

Few things to know for arithmetic addition of two numbers using signed magnitude

Check 1:- If one of the numbers to be added is negative then take signed 2’s complement of the number.

Check 2:- If any ‘end carry’… discard it.

Check 3:- If the MSB of result after discarding ‘end carry’ is 1 then take 2’s complement of the remaining bits

Answer. The arithmetic sum of two numbers +25 and -37 using signed magnitude method is -12 (10001100)  

Sign Bit

1

1

Example 1: Add -37 to +25

+ 25          in signed convention   00011001                             00011001

- 37           in 2’s complement      11011011                             11011011

                                              Equivalent Result: -                   1110100

                                         2’s complement of result                0001100