# Karnaugh map - assign variables to the inputs?

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?

• Could you please label the inputs w,x,y,z in the diagram ? Commented Feb 27, 2014 at 8:16
• Don't use images as main content of your post. Not only is it lazy, it also makes your question impossible to search and inaccessible to the visually impaired; we don't like that. Please transcribe text and maths (note that you can use LaTeX) and don't forget to give proper attribution to your sources!
– D.W.
Commented Feb 27, 2014 at 9:46

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.

• Hey thanks for your answer. The karnaugh map represents the OR-XOR circuit (fig.1) where the input from top to bottom is w,x,y,z. so when w=1,x=0,y=0,z=0 (the top right cell in the map) then F=1. isnt that how the Karnaugh map works? I am unsure on how you get that simplified equation, and I dont know how you get that output equation Commented Feb 28, 2014 at 2:32
• also, isnt the simplified equation wx'y'+yw'x' ? i.imgur.com/AZM3HWp.png Commented Feb 28, 2014 at 4:18
• Yeah, I was wrong. I edited the answer Commented Feb 28, 2014 at 8:33
• @user14864 Yeah, logically that's how Karnaugh Map is to be filled. See some standard logic design book to know how to simplify the Karnaugh Map Commented Feb 28, 2014 at 13:41
• Ok now, how did you find the equation a'b'⋅(c+d)+c'd'⋅(a+b) ? Commented Mar 1, 2014 at 0:53