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EX1:  -7,  -6 : Two negative numbers.

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’b1110) = 1 010, save msb as sign bit and convert lower 3 bits in 2’s complement.

 

 

Signed number addition of two negative numbers and overflow condition.

Step 2: Add & store the result in sum register 5 bits wide.  

   1 001

  1 010

-----------

1 0 011

-----------

 

 

Step 3: No carry into signed bit but carry out of signed bit. In this scenario keep MSB as sign and take 2’s complement of lower 4 bits.

 

Result: 5’b1 1101 = 0x1D = -13

 

Summary in table below

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

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.

Solved Examples for 3 variable Kmaps
1. F(x,y,z) =     (0,1,6,7) - Minimization, on this page.
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3. F(x,y,z) =     (3,4,6,7) - Minimization from here.
4. F(x,y,z) =     (0,1,2,3,4,5,6,7) - Minimization from here.
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