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[Solved]: Karnaugh map - assign variables to the inputs?

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Problem Detail:

I drew the map on the right, but what I drew doesn't work for what the question is asking me. I think I did something very wrong, and I don't really understand what this question is asking me. Am i suppose to re arrange the binary inputs somehow?

Asked By : user14864

Answered By : nitishch

I assume $w,x,y,z$ are inputs to the circuit given. What we need is $$\sum_{w,x,y,z}(2,3,8,9)$$

Put this in a Karnaugh Map and you will get the simplified equation as $w^\prime x^\prime y + wx^\prime y^\prime$. Now, let $a,b,c,d$ be the inputs to the circuit that you have given. Output of first OR gate will be $a+b$. Let it be called $f$. Output of second OR gate will be $c+d$. Let it be called $s$. Output of the XOR gate is $fs^\prime+sf^\prime$. Substitue the values of $f$ and $s$ in the equation and use the equality $(\alpha+\beta)^\prime=\alpha^\prime \beta^\prime$The output will be $$a^\prime b^\prime\cdot(c+d)+c^\prime d^\prime\cdot(a+b)$$.

Compare this with the equation that we require and we find that $$a=w$$$$b=x$$$$c=x$$$$d=y$$ These are the order in which inputs should be given.

Karnaugh Map that you have drawn is correct assuming that $w,x,y,z$ are inputs to the circuit.

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