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So I have been trying to figure this out for about an hour but I am obviously not understanding what I have been reading and watching so I thought I'd ask my own question, I would appreciate a very layman explanation of the following.

I am trying to simplify the following using a K-map

$$F=wxy+yz+x\overline{y}z+w\overline{z}$$

Now I created the truth table and found the midterms associated with it and created a K-map that matches $F$

K-Map

Now my problem is figuring out how to get the simplified function from it. I know I'm supposed to box stuff off so the following is what I did

K-map2

First I tried to compute the 3x3 square which is did the following for:

$$zyzw+xyz\overline{w}+xy\overline{z}w+x\overline{y}zw+xz\overline{yw}+x\overline{yz}w+\overline{x}yzw+\overline{xw}yzw+\overline{xz}yw$$

$$(xyzw+\overline{x}yzw) +(xyz\overline{w}+\overline{xw}yz)+(xy\overline{z}w+\overline{xz}yz)+(x\overline{y}zw+x\overline{yw}z)+x\overline{yz}w$$

$$yzw+yz\overline{w}+y\overline{z}w+x\overline{y}z+x\overline{yz}w$$

$$(yzw+yz\overline{w})+y\overline{z}w+x\overline{y}z+x\overline{yz}w$$

$$yz+y\overline{z}w+x\overline{y}z+x\overline{yz}w$$

Now that's as far as I got from the larger 3x3 square and I'm pretty sure the smaller rectangle on the right is just the following:

$$\overline{z}w$$

now I don't know if I made the correct squares on the K map, and if I did then I don't know if I made the final function small enough, it doesn't seem to be any simpler than the original. If someone could either show me where I went wrong or show me where I can make the function any simpler I would greatly appreciate it.

AFC
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1 Answers1

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A correct version of the K-map is the following:

$$\begin{array}{r|c|c|c|c} \text{wx}\backslash \text{yz}&00&01&11&10\\\hline 00&&&1&1\\\hline 01&&1&1&\\\hline 11&1&1&1&1\\\hline 10&&&1&1 \end{array}$$

When grouping you should only use groups with $2^n$ cells. Make as large groups as possible. And remember that groups can wrap around from a top edge to a bottom edge and from a left edge to a right edge.

The above map can thus be reduced to $3$ groups of $4$ cells each, giving: $$F=w\overline{z}+xz+yz$$ or $$F=w\overline{z}+z(x+y)$$

Jens
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