# How do I simplify this sum of products expression into an easier sop form

'=Compliment

D=P'VST + PV'S'T + PV'ST'+ PV'ST + PVS'T' + PVS'T + PVST' + PVST I'm having trouble simplifying this.

• Have you tried K-maps? – Chris Laplante Nov 19 '13 at 4:18
• The Maxterms can be easily found out from your expression here, and when you have the maxterms, you know the minterms too (The rest of them). Now, as @ChrisLaplante said, use K-maps for SOP simplification. – Anshul Nov 19 '13 at 5:31

For a beginner this is best done with a 4-variable K-map.

I'm a bit rusty on these things but this should help as a start: -

P'VST + PV'S'T + PV'ST'+ PV'ST + PVS'T' + PVS'T + PVST' + PVST becomes

(P'VST + PVST) + P(V'S'T + V'ST' + V'ST + VS'T' + VS'T + VST') which becomes

VST + P(S'T + ST' + V'ST + VS'T') etc..

If we break the terms apart, we have 8 (P'VST -> 1000), 6 (PV'S'T -> 0110), 5, 4, 3, 2, 1, and 0. From those we can combine (via Q-M, which combines values with single-bit differences):

3, 2, 1, and 0 (00XX -> PV)
5, 4, 1, and 0 (0X0X -> PS)
6, 4, 2, and 0 (0XX0 -> PT)
8 and 0 (X000 -> VST)

Putting those together we get PV + PS + PT + VST, which can be simplified even further if desired.

• I don't think this answer is very useful to a beginner. – Chris Laplante Nov 19 '13 at 4:25