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Signed representation by 1’s Complement

1´s Complement Representation

Here, the role of the sign bit is the same as that of the signed magnitude form. Sign bit 0 and 1 represent the positive number and negative number respectively. The magnitude post represents the 1´s complement of the actual number.

Example 1:

Representation of +10 and -10:

Example 2:

- 5 represented by 1’s complement:

First, write + 5 → 0101 then takes its 1’s complement1010 → this represents the -5 in terms of one’s complement.

Properties of 1´s complement representation:

1. 1´s complement representation extends the same hardware for addition and subtraction.

2. 1´s complement is not the weighted system.

3. If a signed number in 1’s complement form is 

Then its decimal equivalent will be   

Where, 

4. With the n bits, the range of numbers that can be represented in 1´s complement representation is 

Example:

If we consider 8 bits, we can represent -127 to +127.

If we consider 4 bits, we can represent Range (-7 to +7).

5. Sign Extension in 1’s complement form:

Here, the sign bit is copied to all the extended positions.

Example:

Representation of -7:   (without sign extension)

Representation of -7 in 8 bits:  (with sign extension)

Question:

A number is represented in 1’s Complement as 100110. Find the equivalent decimal number.

Answer: