K-Maps Prime Implicates and Essential Minterms

1. Feb 12, 2015

Extreme112

1. The problem statement, all variables and given/known data
For each of the following functions with “don’t care” conditions, draw two k-maps: one for the simplified SOP and the other for the simplified POS; circle the essential prime circles, and underline the essential prime minterms (maxterms) as described in lecture. Indicate all prime implicants (implicates) and all essential implicants (implicates).
(a) F(w,x,y,z) = ∑m (0,2,4,6,7,8,12,13), d(w,x,y,z) = ∑m (5,10)

2. Relevant equations
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3. The attempt at a solution

I just want to check if my answers are correct. First one seems like all 0's are essential. And the second one it seems like there are many ways to circle the 1's.

2. Feb 15, 2015

eeestud

to get a more simplified answer we encircle the 1s or 0s with as many same bits(adjacent to it) as possible. So, by this I mean that the best way is to encirlce the largest circles possible. For example, if there are combinations of QUAD and BIN possible, then we essentially choose the QUAD, thereby obtaining a simplified solution.