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$$\begin{array}{cccc} \textbf{X} &\textbf{Y} &\textbf{Z} & \textbf{A}\\ T & T & T & T\\ T & T & F & T\\ T& F& T& F\\ T& F& F& F\\ F& T& T& F\\ F& T& F& T\\ F& F& T& F\\ F& F& F& T\\ \end{array}$$

I'm fairly new to truth tables so please bear with me. I was working on some truth table values and I was doing fine until I came across a truth table with $3$ rows to consider. Can you please help me figure out what expression will give the $A$ values?

Jessie
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sarem dave
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    I am assuming that you want a way of conjuring a formula for $A$, based on each of $X, Y,$ and $Z$. For the general problem, I do not know of any algorithmic approach to simplifying/summarizing the pertinent truth tables entries. With respect to this particular truth table, I was unable to create any elegant formula for $A$, based on $X,Y$ and $Z$. – user2661923 Mar 15 '21 at 22:03

1 Answers1

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Use a 3-input (4x2) Karnaugh map:

https://en.wikipedia.org/wiki/Karnaugh_map

With (X,Y) indexing the rows, and Z indexing the columns.

You should end up with two clusters of two $T$s.

Each cluster allows you to treat one of the 3 inputs as a "don't care" for that cluster (e.g. $Z$ might be a "don't care"). The AND of the two other two input variables in a cluster (e.g. maybe $X$ and $Y$), gives you the expression for the cluster, e.g. $X\cdot Y$

The OR of all of the cluster expressions gives you the overall expression.

You should end up with $$ A = X \cdot Y + X' \cdot Z' $$ or something equivalent.

Andy Walls
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