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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’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  
Carry into signed bit and carry out of signed bit. 
11 
no 
Sign 
value 
 
No carry into signed bit and no carry out of signed bit. 
00 
no 
Sign 
Bit[3] = 1 so take 2’s complement. 
 
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: 
EX2: +7, 
EX3: 
EX4: +7, +6 : Two positive numbers