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Digital Basics Tutorial.

Add two signed numbers examples below.

EX1:  +7,  +6 : Two negative numbers.

 

+7  +6

Step 1: Convert to 2's complement for negative numbers.

 

+7 (in Binary 4’b0111)

+6 (in Binary 4’b0110).

Step 2

Add and store the result in sum register of 5 bits wide.  

    0 111

   0 110

-----------

0  1 101

-----------

 

Step 3

Carry into signed bit but no carry out of signed bit. In this scenario keep MSB as sign and lower 4 bits represent sum.

Result: 5’b0 1101 = 0x0D = 13

 

 

 

Summary Table

Values

Observations

2 bit Binary representation for [1] carry in, [0] carry out

Use Bit[4] as sign for overflow

Bit[3] as sign, value, 2’s complement.

Bit[2:0] as value or 2’s complement.

 

+7 +6

Carry into signed bit but no carry out of signed bit.

10

Yes

value

value

+7 -6

Carry into signed bit and carry out of signed bit.

11

no

Sign

value

-7 +6

No carry into signed bit and no carry out of signed bit.

00

no

Sign

Bit[3] = 1 so take 2’s complement.

-7 -6

No carry into signed bit but carry out of signed bit.

01

Yes

Bit[4] =1 so take 2’s complement.

 

Bit[4] = 1 so take 2’s complement.

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