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Boolean Simplification Help

  1. Oct 3, 2008 #1
    1. The problem statement, all variables and given/known data
    We have been given a task to develop a circuit which displays the square of a binary number on a 3 x 7 seq displays.

    I have already gone through and done up the Karnaugh Maps for the task and have identified the minterms. However, I believe that these can still be simplified even more.

    2. Relevant equations
    Karnaugh Maps Output = A'B'CD + A'BC'D + A'BCD' + ABCD + B'C'D' + AB'C'


    3. The attempt at a solution
    A'B'CD + A'BC'D + A'BCD' + ABCD + B'C'D' + AB'C'
    Factor out A' and C from minterms 1 and 3
    a'c(b' + b) (d + d')
    = a'c + a'bc'd + abcd + b'c'd' + ab'c'
    Factor out B and D from minterms 2 and 3
    bd(a' + a)(c' + c)
    = a'c + bd + b'c'd' + ab'c'(Can I simplify this anymore???)
    Can the minterm ab'c' absorb the minterm b'c'd' ???
    Also by using the distributive law can I add B to the minterm a'c and then further simplify the equation???

    Thank you for any assistance...
     
    Last edited: Oct 4, 2008
  2. jcsd
  3. Oct 5, 2008 #2
    I just had another look through and have come up with a different break down of the karnaugh maps

    3. The attempt at a solution
    A'B'CD + A'BC'D + A'BCD' + ABCD + B'C'D' + AB'C'
    Factor out A' and D from minterms 1 and 2
    A'D(b' + b) (c + c')
    = A'D + A'BC'D + ABCD + B'C'D' + AB'C'
    Factor out B and D from minterms 2 and 3
    bd(a' + a)(c' + c)
    = A'D + BD + B'C'D' + AB'C'

    This is where I am getting stuck. Is it possible to further simplify the equation or is this the final solution???

    or

    Can I do the following???

    Factor out D from minterms 1 and 2
    D(A' + B) + B'C'D' + AB'C'
    A'D + B + B'C'D' + AB'C'
     
    Last edited: Oct 5, 2008
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