# Representation of Negative Numbers: Sign-Magnitude, Sign-1՚s Complement, and Sign-2՚s Complement (Especially for GATE-Geospatial 2022)

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When we subtract a larger number from a smaller one, the result is negative. Let us examine, with the help of example, whether the computer can distinguish between a positive and a negative result.

### Example

Subtract 9 from 7 in binary, using and 2՚s complement addition method for subtraction.

Now,

(Minuend)

(Subtrahend)

And 2՚s complement of the subtrahend is 10111.

Therefore,

Now it is clear that the computer will not be able to recognize the negative result. For this reason, an additional bit, called sign bit, is used on the left of the MSB of the number to indicate its sign.

## Methods of Representing Negative Numbers

There are three methods for representing negative numbers. In binary system they are as follows:

- In sign-magnitude method
- In sign-1՚s complement method
- In sign-2՚s complement method

The relative merits and demerits of the methods may be examined with the help of the following example.

Represent in three different methods of representing negative numbers and add to it in each case. Consider

## (I) in Sign-Magnitude Method

is represented as

is represented as

Adding together we get

The result of adding and should be 0 and it should have been represented as .

## (II) in Sign-1՚s Complement Method

is represented as

is represented as

Adding together we get

Here also, we see that the data 0 (0,00000) and arithmetic 0 are not the same, and so it is also not suitable for performing arithmetic operation.

## (III) in Sign-2՚s Complement Method

is represented as

is represented as

Adding together we get

Here, we see that the data 0 and arithmetic 0 are the same, and so it is convenient for performing binary arithmetic operation.