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Question
Reduce the Boolean function F(P,Q,R,S) = (P+Q+R+S) • (P+Q+R+Sꞌ) • (P+Q+Rꞌ+S) • (P+Qꞌ+R+S) • (P+Qꞌ+R+Sꞌ) • (P+Qꞌ+Rꞌ+S) • (P+Qꞌ+Rꞌ+Sꞌ) •(Pꞌ+Q+R+S) • (Pꞌ+Q+R+Sꞌ) by using 4-variable Karnaugh map, showing the various groups (i.e. octal, quads and pairs).
Solution
There are three quads:
Quad 1: ( M0 M1 M8 M9) = Q + R
Quad 2: ( M4 M5 M6 M7) = P + Q’
Quad 3: ( M0 M2 M4 M6) = P + S
Hence F(P,Q,R,S) = (Q + R) . (P + Q’) . (P + S)
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