# Signed Binary Number

signed binary number can be represented in one of the three ways

1. Signed magnitude representation
2. 1’s complement representation
3. 2’s complement representation

Signed magnitude representation :

1. If the data has positive as well as negative numbers then the signed binary number should be used.
2. the + or – signs are represented in the form of binary by using 0 or 1. So 0 is used to represent the ( + ) sign and 1 is used to represent the ( – ) sign.
3. the MSB of a binary number is used to represent the sign and the remaining bits are used to represent the magnitude.

8-bit signed binary numbers are shown in fig (a) Positive binary number (b) Negative binary number

8-bit signed binary numbers

1. the main advantage of sign magnitude number is their simplicity.
2. we can easily find the magnitude by deleting the sign bit.

Disadvantage of sign magnitude numbers:   sign magnitude numbers have a limited use because the require complected circuits. these numbers are often used in analog to digital converter.

Complements:  Complements are used in the digital computer. it is used to simplify the subtraction operation and for the logical manipulations.

* Note:- we take 1’s and 2’s complement only -ve numbers not +ve numbers.

 Decimal Signed 2’s complement Signed 1’s complement Signed magnitude + 7 0111 0111 0111 + 6 0110 0110 0110 + 5 0101 0101 0101 + 4 0100 0100 0100 + 3 0011 0011 0011 + 2 0010 0010 0010 + 1 0001 0001 0001 + 0 0000 0000 0000 – 0 — 1111 1000 – 1 1111 1110 1001 – 2 1110 1101 1010 – 3 1101 1100 1011 – 4 1100 1011 1100 – 5 1011 1010 1101 – 6 1010 1001 1110 – 7 1001 1000 1111 – 8 1000 — —

Signed Binary Number

Signed Binary Arithmetic:- Addition in 2’s complement method there are four cases

1. Both numbers are +ve

2. +ve number and smaller -ve number

3. +ve number and larger -ve number

4. both number are -ve.

Case 1: Addition of both positive number: Case 2:  +ve number and smaller -ve number:

1. find the 2’s complement of the smaller -ve number
2. Add the +ve number with 2’s complement of smaller -ve number.
3. The above sum must produse a carry. this carry is always discarded and the remaining bits give the +ve sum.

Let A = + 22 and B = -17 Case 3:- +ve number adds with larger -ve number

1. find the 2’s complement to the larger -ve number
2. Add the +ve number with 2’s complement of larger -ve number
3. the above addition does not produce any carry. the result is a -ve number in the form of 2’s complement representation.

####  Case 4:- Both number have -ve number:-

1. Both -ve number are represented in 2’s complement
3. the remaining bits are the result of above addition in the 2’s complement representation.

Example:-  -9 and  -4  