Simplifying Boolean Function

Question

I am in a computer class with Karnaugh Maps and one of the questions is X 'Y Z + X 'Y 'Z + 'X Y 'Z + X Y Z and I need to simplify it

where ' means not so 'x means not x.

I think the answer is X 'Y + X Z + 'X Y 'Z but I am not sure, if I am wrong can anyone correct me or tell me if this is the correct answer.

Also is it possible to turn a Boolean function into a Karnaugh Map?

X 'Y Z + X 'Y 'Z + 'X Y 'Z + X Y Z to a Karnaugh Map, I am wondering because that is what i did to get that answer above, but I am not sure if it is allowed.

edit: can a kmap like this be used to solve it?

xyz 00 01 11 10

0 1 1 1 1 1

Try this neat website, which is able to transform Boolen formulas into DNF and CNF: http://www.izyt.com/BooleanLogic/applet.php — Florian, Mar 03 '15 at 14:30

amWhy · Answer 1 · 2013-10-06T18:00:05.950

2

There's an error in your proposed answer:

I'll use the prime $'$ immediately following the variable, so that $X' = \text{not}\; X$. I use the distributive law twice: $ab + ac = a(b+c)$, and then I use the identity that $a + a' = 1$:

$$\begin{align} X Y' Z + X Y' Z' + X' Y Z' + X Y Z & = XY'(\underbrace{Z + Z'}_{\large =1}) + Y(X'Z' + XZ) \\ \\ & = XY' + Y(X'Z' + XZ)\end{align}$$

Or, equivalently $XY' + X'YZ' + XYZ$

edited Oct 06 '13 at 18:00

answered Oct 06 '13 at 17:54

amWhy

209,954

so is it not possible to use a kmap? – Tom Oct 06 '13 at 18:22
@amWhy: Needs a TU! +1 – Amzoti Oct 07 '13 at 04:34
Your solution is the same as his. $XY'Z$ is included in $XY'$ so $XY'+XYZ=XY'+XZ$ – Empy2 Mar 03 '15 at 14:38

Simplifying Boolean Function

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