Karnaugh map solution verification

Question

Find the minimal form of the logical expression in its DNF form as \begin{equation*} d=x'y'z'+x'yz'+x'yz+xyz' \end{equation*}

My answer:

After grouping $(1,3),(1,4)$ and $(1,4),(2,4)$ cells as doubles and $(1,1)$ cell as single, I obtain the minimal form as \begin{equation*} d=x'y'z'+x'y+yz' \end{equation*} But the answer is $x'z'+x'y+yz'$.

Where am I doing wrong?

score 1 · Answer 1 · answered Apr 25 '21 at 12:09

1

The Karnaugh map is a torus, so a rectangle containing $x'y'z'$ can be extended to the other side, becoming $x'z'$.

answered Apr 25 '21 at 12:09

Parcly Taxel

103,344

Can you please elaborate this? I don't know torus. – Manjoy Das Apr 25 '21 at 12:17
Is my answer also correct? – Manjoy Das Apr 25 '21 at 12:19
So how do I know that further simplification is possible? – Manjoy Das Apr 25 '21 at 12:21
So can every single group be extended to the furthest corner in that row or column? – Manjoy Das Apr 25 '21 at 12:24
@ManjoyDas It is mere pattern recognition. – Parcly Taxel Apr 25 '21 at 12:25
it's quite fishy – Manjoy Das Apr 25 '21 at 12:29

Karnaugh map solution verification

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