Product of Sums Simplification (3.5)

·         Use sum-of-products simplification on the zeros of the function in the K-map to get f’.

·         Recall that the complement of a boolean function can be obtained by (1) taking the

dual and (2) complementing each literal. (aka generalized DeMorgan’s rule).

·         Complement f’ using DeMorgan’s Theorem to get f.

Example

·         Find a simplified product-of-sums expression for f(a,b,c,d) = M(0,1,7,15).

·         (f(a,b,c,d))’ =a’b’c’ + bcd

·         f_dual (a,b,c,d) = (a’+b’+c’)(b+c+d)

·         f(a,b,c,d) = (a+b+c)(b’+c’+d’)