Question

) Simplify the following Boolean functions by first finding the essential prime implicants (Please indicate the essential prime implicants and prime implicants): (a) F(w, x, y, z) = S(0, 1, 2, 4, 5, 6, 8, 10, 13, 15) (b) F(w, x, y, z) = wy’ + xy + y’z + w’xz

Answer 1

Essential Prime Implicants –

These are those values which cover atleast one minterm which cannot be covered by any other prime implicant. Essential prime implicants(EPI) are those prime implicants which must appear in final solution.

(a) F(w, x, y, z) = S(0, 1, 2, 4, 5, 6, 8, 10, 13, 15)

Prime Implicants - w’y’, w’yz’,wxz’, wx’z

Essential prime implicants - w’x’y’z’, w’x’y’z, w’x’yz’, w’xy’z’, w’xy’z,

                         

w’xyz’, wxy’z’, wxyz’, wx’y’z, wx’yz

(b) F(w, x, y, z) = wy’ + xy + y’z + w’xz

Prime implicants - y’z, wx, xy, wy’

Essential prime implicants - wx’y’z’, w’x’y’z, w’xy’z, w’xyz, w’xyz’, w’y’, w’yz’, wxz’,wx’z