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Signed numbers in Decimal

4 bit Signed Representation.

bit[3] = signed value,

bit[2:0] = value after sign bit

bit[3] = 1 when sign ‘-

bit[3]=0 when sign ‘+’

Representation of negative numbers as 2’s complement.

bit[3:0] = value.

bit[4] as 0.

7

4’b0111

UNCHANGED

6

4’b0110

 

5

4’b0101

 

4

4’b0100

 

3

4’b0011

 

2

4’b0010

 

1

4’b0001

 

0

4’b0000

 

-1

4’b1001

3’b111

-2

4’b1010

3’b110

-3

4’b1011

3’b110

-4

4’b1100

3’b100

-5

4’b1101

3’b011

-6

4’b1110

3’b010

-7

4’b1111

3’b001

Binary addition of signed numbers

Signed number is a way of representing positive & negative numbers in binary form where most significant bit(MSB) signifies sign.

In table below positive and negative numbers in range -7 to +7 are represented in column 1. The column 2 is signed representation.  Where as the column three is for 2’s complement equivalent of negative numbers. The 2’s complement conversion is a crucial requirement for binary addition involving signed numbers.  Lets review it in table below.

Examples related to signed magnitude are discussed next.

Examples to add four possible combinations of two signed numbers.

EX1:  -7,  -6 : Two negative numbers.

EX2: +7,  -6 : Positive greater than negative.

EX3:  -7, +6 : Negative greater than positive.

EX4: +7, +6 : Two positive numbers

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Sign_magnitude.