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The boolean expression z+w' is received after simplification of the expression

vw'y+v'wz+vyz+v'w'x'y'+v'w'xyz+vw'y'z'+vw'xy'z+v'w'yz'

We don't know what are the don't care numbers, what are the numbers that are for sure don't care expressions?

I tried solving this a few ways, but none of them worked. I find it more important for me to understand the way to solve this question, so please provide a detailed answer.

I tried to use a truth table with 5 variables, and then a Karnaugh map, but I'm still struggling.

Thanks.

BOB123
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1 Answers1

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Hint

Set up a Karnaugh map with $vwx$ on top and $yz$ on the side, like this:

$$\begin{array}{r|c|c|c|c|c|c|c|c} \text{vwx}\backslash \text{yz}&000&001&011&010&110&111&101&100\\\hline 00\\\hline 01\\\hline 11\\\hline 10 \end{array}$$ Now fill in the map with 1's in the places given by the larger expression. In order for the larger expression to reduce to z+w', there must be 1's or "don't care"s in row 2 and 3 as well as in columns 1,2,7,8.

You will find that 6 "don't care"s are needed.

Jens
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  • Hi, many thanks for the answer but that's what I have tried. for example: if I take a look at the larger expression and I choose the first number combination it gives me $vw'y = 101 = 5$ then i mark it in the table at the place of number 5 as 1 right?

    then I fill the rest of the numbers same technique as mentioned above...

    if that's the way, then what's next?

     – BOB123 Jul 22 '18 at 06:19
  • First, don't think of the bit combinations as numbers, just as bit combinations. Second, the columns give combinations of $vwx$, not $vwy$. So in which columns is $vw=10$? And in which rows is $y=1$? Put a 1 in the intersection of those columns and rows. Continue in the same way with the rest of the expression. – Jens Jul 22 '18 at 06:48
  • Ok got you, i made my K-map as $vw$ rows and $xyz$ columns but lets do your way!. but the example you give me there are 2 options to put 1 for $vw=10$ and $y=1$ how can i know which one of them? – BOB123 Jul 22 '18 at 16:36
  • Put 1 in all of them. – Jens Jul 22 '18 at 19:24
  • Many thanks! sometimes all you need is to put it in the tables and the answer is in front of your eyes. – BOB123 Jul 22 '18 at 20:52