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Simplifying equations using boolean algebra

  1. Apr 30, 2009 #1
    I need to simplify these boolean expressions.

    1. The problem statement, all variables and given/known data

    Problem A:
    a`b`d+a`bd`+bc`d`+bcd`+ab`c`d+b`cd

    Problem B:
    a`b`cd+a`bd+abcd+a`b`d+acd+abd+ab`c`d

    Problem C:
    a`b`c`d`+a`b`cd`+a`bd+ab`c`d`+bd+ab`d`


    2. Relevant equations

    abc means a AND b AND c
    a+b means a OR b
    a` means NOT a



    3. The attempt at a solution

    I have been working on these for over 6 hours and I still have a mess. I look at the rules and try to apply them, but I know my answers are incorrect.
     
    Last edited: Apr 30, 2009
  2. jcsd
  3. Apr 30, 2009 #2

    tiny-tim

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    Welcome to PF!

    Hi mrlupr! Welcome to PF! :smile:

    Let's start with …
    The bc`d`+bcd`part is easy …

    what is that? …

    and how much further can you get?

    Hint: try grouping together all the terms with b`d :wink:
     
  4. May 1, 2009 #3
    here is what I have so far.

    bc`d`+bcd`
    bbc`+cd`d`
    bc`+c`d
    c`+bd

    how does it look?
     
  5. May 1, 2009 #4

    tiny-tim

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    sorry … i've no idea what you're doing :confused:
     
  6. May 1, 2009 #5
    Ok how about this

    bc`d`+bcd`
    bd`(c`+c)
    bd`1

    am I any closer?
     
  7. May 1, 2009 #6

    tiny-tim

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    Yes, that's it!

    But write it with = signs, and there's no need to write 1 …

    bc`d`+bcd`
    = bd`(c`+c)
    = bd` :smile:

    ok, now have a go at all the b`d terms :wink:
     
  8. May 1, 2009 #7
    Ok lets go

    a`b`d+a`bd` +bd`+ ab`c`d+b`cd`
    =a`11+bd`+ab`d
    =a`+ab`d+bd`
    =b`d+bd`

    How does it look?
     
  9. May 1, 2009 #8

    tiny-tim

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    again … no idea what you're doing :confused:
     
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