Need help simplifying a boolean expression using algebraic theorems/postulates only

Question

Suppose I have this boolean expression:

W'XYZ + WX'YZ + WXY'Z + WXYZ' + WXYZ

How would I go about simplifying this without using a K-map? Using K-map, the simplified form is XYZ + WXY + WXZ + WYZ. I read about the redundancy theorem somewhere, would rather not use that as well.

Bram28 · Accepted Answer · 2017-10-08T02:43:39.680

0

Here is a good law for you to use:

Adjacency

$PQ +PQ'=P$

It's called Adjacency because if you were to put it on a K-map, the two terms in the left hand side would pick out cells that are adjacent in the K-Map and that can be combined into one larger group of cells ... hence the much simpler expression.

edited Oct 08 '17 at 02:43

answered Oct 08 '17 at 02:39

Bram28

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I'm guessing saying W'XYZ + WXYZ = XYZ is an example of this law in action? I'm clueless with regards to simplifying the other three terms though, since we lose the WXYZ after this first step. – Sanchit Batra Oct 08 '17 at 02:41
@SanchitBatra yes, it is ... and you can always copy terms using $P=P+P$ so you don't 'lose' them. – Bram28 Oct 08 '17 at 02:44
That's exactly what I was looking for, thank you so much! – Sanchit Batra Oct 08 '17 at 02:45
@SanchitBatra Glad I could help! :) – Bram28 Oct 08 '17 at 02:47

Need help simplifying a boolean expression using algebraic theorems/postulates only

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