Simplifying boolean expression inconsistency.

Discussion in 'Homework Help' started by sini, Sep 30, 2011.

  1. sini

    Thread Starter New Member

    Jun 28, 2010
    6
    0
    Hello,

    Is it possible to simplify algebraically y = !C(!A!B!D + D) + A!BC + !D
    into y = !C + !D + !BA

    If I use the method of transforming the question first into Sum-of-Products form and then entering each term into Kmap I will obtain the above simplification after reading off the 1s, but, if I just use algebraic method instead I can never reach this result and instead produce
    y = !C + !D + !B(!A!C + AC) but by simple truth table it is obvious A =/= XNOR which AC + !A!C is.

    My algebraic derivation:
    y = !C(!A!B!D + D) + A!BC + !D
    y = !C(!A!B + D) + A!BC + !D
    y = !A!B!C + !CD + A!BC + !D
    y = !C + !D + !B(AC + !A!C) as oppose to y = !C + !D + !BA

    I can get the y = !C + !D + !BA result if I put y = !C + !D + !B(AC + !A!C) terms into Kmap and read solution from there, but shouldn't there be a way to arrive at the answer just by using algebra laws?

    Thank you for reading.
     
  2. Zazoo

    Member

    Jul 27, 2011
    114
    43
    You have:
    y = !C + !D + !B(AC + !A!C)

    Rather than factoring !B, leave it as:

    y = !C + !D + !BAC + !B!A!C

    You can eliminate the fourth term completely since you have !C as the first term, giving:

    y = !C + !D + !BAC

    From here !BAC reduces to !BA (again, because of the !C term). This gives you your K-map answer.
     
  3. sini

    Thread Starter New Member

    Jun 28, 2010
    6
    0
    ah, thank you :)
     
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