Another boolean equation

Discussion in 'Homework Help' started by Blue_turnip, Mar 13, 2007.

  1. Blue_turnip

    Thread Starter New Member

    Mar 5, 2007
    8
    0
    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.
     
  2. Dave

    Retired Moderator

    Nov 17, 2003
    6,960
    144
    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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