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I have a question regarding the process of finding minterms.

Problem: Find the minterms of the following expression by first plotting each expression on a K-map:

a) F(X,Y,Z) = XY + XZ + X’YZ
b) F(W,X,Y,Z) = XZ + W’XY’ + WXY + W’YZ + WY’Z 
c) F(A,B,C,D) = B’D' + ABD + A’BC

Is there any way that I can find the minterms of function without making a truth table? Like can you just look at the boolean expression and plot the 1's for the minterm on a k-map?

CapturedTree
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2 Answers2

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Take $F(A,B,C,D) = BD + \dots$

In the K-map, addition is the union of each terms. The first term being the intersection of $B$ with $D$ (i.e. logically both B and D are true).

The $B$ is represented by two rows, $\bar{A}B$ and $A B$ since $(\bar{A}+A) B = B$. Similarly, $D$ is represented by two rows, as shown.

After we fill the k-map for all terms, we can visually read the minterms from their locations in the k-map. If $F(A,B,C,D) = BD$ as below, then $F = \bar{A}B\bar{C}D + \bar{A}BCD + AB\bar{C}D + ABCD$, (i.e. true for inputs 0101, 0111, 1101, 1111).

enter image description here

Weaam
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    That was a great explanation Weaam. Thank you so much! I am still trying to wrap my head around this, but I completely understand your solution. I feel like I just need to practice a little more with k-maps! – CapturedTree Oct 04 '15 at 03:52
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    Thank you. Even if your ultimate goals are more abstract, you might consider working through examples/exercises of "Digital Design, M. M. Mano, ch. 3" and "Principles of Modern Digital Design, P. K. Lala, ch. 3". Best regards. – Weaam Oct 04 '15 at 04:14
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You can use boolean algebra simplification laws for reducing variables, but the K-map will give you exactly the minterm, for what I know there is no other way to solve it.

D. A.
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