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Signed Number Representation       

Signed Number representation

1. Signed magnitude (+ve and -ve)

2. 1´s complement (+ve and -ve)

3. 2´s complement (+ve and -ve)

Signed Magnitude Representation:

Signed magnitude representation is the representation system used for signed binary numbers in which MSB (Mist Significant bit) represents the sign of the number and the remaining bits represent the magnitude of the number.

Sign Bit: 

MSB of a signed binary number is called the sign bit.

Then

The equivalent decimal of the number will be

Example:

Representation of (+10) in signed magnitude

Representation of (-10) in signed magnitude

Properties of Signed Magnitude representation:

1. Signed magnitude requires separate hardware for addition and subtraction.

2. Signed magnitude is the weighted system, where weight is applied on all bits except the sign bit.

3. With n bits, the range of numbers that can be represented in signed magnitude form is

Example:

Here 8 bits, we can separate numbers from,

Example:     

Lets for 4-bit representation

Truth Table:

1. Sign Extension is signed magnitude:

The sign extension provides the facility to store the smaller number in a larger register without changing either the value of the sign of the number. In signed magnitude, the signed bit is moved to the most significant position.

Example:

Example:

Representation of -7; (without sign Extension)

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

Question:

One sign number represents  101101. Find the equivalent decimal.

Solution:

Note: 

For +13 representation (001101) or (01101) [0 indicates sign bit]

Question:

Represent -4 sign number. Find the equivalent 8-bit binary number. 

Solution:

Here if represent -4 in 4 bit:  (sign) 1 100

Now we can represent -4 in 8 bit: