Simplifying boolean expression inconsistency.

Thread Starter


Joined Jun 28, 2010

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.


Joined Jul 27, 2011
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.