Question

Convert the following expression to SOP form
F= (W+X) Y*Z) (W+YXX*Y*Z)

Answer 1

Given Expression

F= (W+X) Y*Z) (W+YXX*Y*Z)

F= (W+X) YZ(W+XX*YY*Z)

F= (W+X) YZ(W+X*Y*Z) { We know that PP= P }

F= (W+X) YZ(W+XYZ)

F= (W+X) (WYZ+XYYZZ) { By Distributive law P(Q+R) = PQ+PR }

F= (W+X) (WYZ+XYZ) { We know that PP= P }

F= W(WYZ+XYZ)+X(WYZ+XYZ) { By Distributive law P(Q+R) = PQ+PR }

F= (WWYZ+WXYZ)+(WXYZ+XXYZ)   { By Distributive law P(Q+R) = PQ+PR }

F= (WYZ+WYZ)+(WXYZ+XYZ) { We know that PP= P }

Which is Required expression in SOP form

Simplifed SOP form:

From the above SOP form F= (WYZ+WYZ)+(WXYZ+XYZ)

F= (WYZ+WYZ)+XYZ(W+1) { By Distributive law PQ+PR = P(Q+R) }

F= (WYZ)+XYZ(1) { We know that 1+P= 1 & P+P= P }

F= WYZ+XYZ

Which is Required Simplified Expression in SOP Form