The minterms of functions FA B C and GA B C are Pm1 3 5 6 an

The minterms of functions F(A, B, C) and G(A, B, C) are Pm(1, 3, 5, 6) and Pm(1, 4, 5, 7).

(a) What are the minterms of F\' and G\' ?

(b) What are the maxterms of F + G and F G?

(c) Algebraically express F and G as a product-of-maxterms.

Solution

F(A,B,C) = A\'B\'C + A\'BC + AB\'C + ABC\'

G(A,B,C) = A\'B\'C + AB\'C\' + AB\'C + ABC

a) Min-terms of F\' = Pm(0,2,4,7) [ since all these min-terms were not available in function F)

Min-terms of G\' = Pm(0,2,3,6) [ since all these min-terms were not available in function G)

b) Min-terms of (F+G) = Pm(1,3,4,5,6,7}

Max-term represntation of (F+G) = Maxterm(0,2)

Min-term of (FG) = Pm(1,5)

Max-term represntation of (FG) = Maxterm(0,2,3,4,6,7)

c) F will be represnted as Max-terms(0,2,4,7)

F = (x + y + z ) ( x + y\' + z) (x\' + y + z) (x\' + y\' + z\')

G will be represnted as Max-terms(0,2,3,6)

F = (x + y + z ) ( x + y\' + z) (x + y\' + z\') (x\' + y\' + z)