Develop a ProductofSums POS Boolean Algebra expression for t

Develop a Product-of-Sums (POS) Boolean Algebra expression for the following truth table which shows .

Y =f(A,B,C)

A

B

C

Y

0

0

0

0

0

0

1

1

0

1

0

1

0

1

1

1

1

0

0

1

1

0

1

0

1

1

0

1

1

1

1

1

Solution

First we will derive the sum of product representation from the truth table:

Y= A\'B\'C + A\'BC\' + A\'BC + AB\'C\' + ABC\' + ABC = sum (m(1,2,3,4,6,7))

in product of sum representation:

Y = product ( M(0,5)) = ( A + B + C )( A\' + B + C\' )