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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’b1111) = 1 001, save msb as sign bit and convert lower 3 bits into 2’s complement.

+6 (in Binary 4’b0110).

Step 2

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

   1 001

  0 110


  1 111



Step 3

No carry into signed bit and no carry out of signed bit. In this scenario keep MSB as sign and take 2’s complement of lower 3 bits.


Result: 4’b1 001 = 0x11 = -1



Pos > Neg.
Pos Pos.

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