[Computer Hardware]

Question:

Write the canonical Product-of-Sum (POS) expression for the
Sum and Carry of a Full Adder.

Question

[Computer Hardware]

Question:


Write the canonical Product-of-Sum (POS) expression for the 
Sum and Carry of a Full Adder.

Accepted Answer

Answer:

Sum (S):


S(A,B,C) = ΠM(0,3,5,6)


Carry (C):


C(A,B,C) = ΠM(0,1,2,4)


Explanation:


A Full Adder has three inputs:



A, B, C (Carry input)



and two outputs:



    Sum (S)
    Carry (C)


Truth Table of Full Adder:


A B C | S CARRY

0 0 0 | 0   0
0 0 1 | 1   0
0 1 0 | 1   0
0 1 1 | 0   1
1 0 0 | 1   0
1 0 1 | 0   1
1 1 0 | 0   1
1 1 1 | 1   1


Canonical POS Form:


In Product-of-Sums (POS), we take the rows where output is 0.


For Sum (S):


Output S = 0 for rows:



0, 3, 5, 6



Therefore:



S(A,B,C) = ΠM(0,3,5,6)


For Carry (C):


Output Carry = 0 for rows:



0,1,2,4



Therefore:



C(A,B,C) = ΠM(0,1,2,4)


Conclusion:


    Canonical POS uses maxterms where output = 0

    
        Sum:
        ΠM(0,3,5,6)
    

    
        Carry:
        ΠM(0,1,2,4)

[Computer Hardware] Question: Write the canonical Product-of-Sum (POS) expression for the Sum and Carry of a Full Adder.

Answer with Explanation

[Computer Hardware]

Question:

Write the canonical Product-of-Sum (POS) expression for the Sum and Carry of a Full Adder.