# Another boolean equation

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#### Blue_turnip

Joined Mar 5, 2007
8
Hi guys, (and girls, i should be politically correct).

I have a really hard boolean equation to simplify and I was hoping to get some help.

This is the original equation:

S'P'DF'M'B + S'P'DF'MB' + S'PD'F'M'B + SP'D'FM'B' = Q

Here is my simplification thus far:

DS'P'F'(M'B + B'M) + S'PD'F'M'B + SP'D'FM'B' = Q
DS'P'F'(M'B + B'M) + D'M'(S'PF'B + SP'FB') = Q
D(S+P+F)'(M'B + B'M) + (D + M)'(PB(S+F)' + SF(P+B)') = Q

Is this as simple as it gets? Perhaps there is another 'path' I could have taken which would have let me get it even simpler yet I have tried and tried and can't figure it out. Care to lend a helping hand?

Much appreciated,
Oliver Adams.

I should mention that I am going to make it a circuit. Its second nature for me to try and get things into brackets and even though that may not make the circuit any simpler I tend to do it anyway.

#### Dave

Joined Nov 17, 2003
6,970
The derivation seems fine, and I wouldn't suggest that you can go any further.

I do question why. Assuming you have the complements available:

S'P'DF'M'B + S'P'DF'MB' + S'PD'F'M'B + SP'D'FM'B'

Requires
- 4x6-I/P AND gates
- 1x4-I/P OR gate

D(S+P+F)'(M'B + B'M) + (D + M)'(PB(S+F)' + SF(P+B)')

Requires:

- 1x3-I/P OR gate
- 6x2-I/P OR gates
- 7x2-I/P AND gates
- 1x3-I/P AND gate

Plus a series of inverters for the intermediate complements and some gates I have probably missed.

Dave

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