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.
Best Answer
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.