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The question is to simplify

$$xy'z+wxy'z'+wxy+w'x'y'z'+w'x'yz'$$

Using K-map, the answer is $wx + w'x'z' + xy'z$

However, the question wants me to simplify algebraically, stating laws beside.

I tried it for hours but it's just so hard I can't do it by myself.

It's due tomorrow So I need help please..

Thank You!

Cameron Williams
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SMLJ
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2 Answers2

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I don’t want to say too much, since it’s an assignment, but here’s a rough roadmap.

Notice that the terms $w'x'y'z'$ and $w'x'yz'$ have three factors in common, so you can use a distributive law to pull them out and reduce $w'x'y'z'+w'x'yz'$ to $w'x'z'(y'+y)$, which you should be able to simplify using two laws.

The next bit is the tricky part. Use an absorption law to expand $xy'z$ to $xy'z+wxy'z$. Then simplify $wxy'z+wxy'z'$, and combine the result with $wxy$.

Brian M. Scott
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xy′z+wxy′z′+wxy+w′x′y′z′+w′x′yz′

(w'+w)xy′z + wxy′z′ + wxy +w′x′y′z′ + w′x′yz′ -> multiply first minterm with (w'+w)

w'xy'z + wxy'z + wxy'z'+ wxy +w′x′z'(y'+y) -> reduce last two minterms

w'xy'z + wxy'(z+z') + wxy + w'x'z' -> group 2 and 3rd minterms

w'xy'z + wxy' + wxy + w'x'z' -> 2 min term reduces

w'xy'z + wx(y'+y) + w'x'z' -> group 2nd and 3rd minterm, and reorder minterms

wx + w'x'z' + w'xy'z

I think the last minterm in your answer is wrong.

Raghuraman R
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  • I generated my answer with circuits and truth tables with the original expression, my answer has identical outputs as the question... I dont know your work looks great but there may be something wrong and I can't even spot it.. – SMLJ Jan 28 '15 at 05:32