Why use karnaugh map

Specifically, here are the "rules" for K-map groups that ensure each one corresponds to a single AND gate:. To make sure that we get a minimized SOP formula for the entire function, we must also ensure that:.

We can also do a K-map for 4 variables or more! Below is a 2x2 K-map for 4 input variables. Note that there is still only one output for a single K-map; if you have more outputs in your circuit, you need to do a different K-map for each output.

Here is an example truth table with 5 input variables:. Now that there are 32 truth table entries, we split the K-map into two parts depending on the first variable.

Here's what that looks like:. Now when we make groups, we have one more dimension to make the groups bigger - by having the same group on both sides of the K-map. In this case, we can group the second row on each side. A second group goes over the middle two columns of the right side:.

For many kinds of circuits, there are certain combinations of inputs which are impossible for some reason. Then we don't care what the output is in those cases, because we can assume those inputs will never happen. We draw these as an "X" in the truth table and the K-map. These can have either a 0 or 1, whichever helps the minimization. With don't-cares, we must cover all the 1's, but we don't have to cover all the X's.

And the X's can be part of a group, or not. In this case, we can cover all the 1's, without including any 0's, by just making one group for the first column and one group for the third row. That leaves one X inside a group, and one out of the groups, which is fine because we don't care what the X's are. Introduction of Boolean Algebra and Logic Gates. Combinational Circuits.

Sequential Circuits. Number Representation and Computer Airthmetic. Table of Contents. Save Article. Improve Article. Like Article. Previous Functional Completeness in Digital Logic. Next Various Implicants in K-Map. Recommended Articles. Article Contributed By :. Easy Normal Medium Hard Expert.

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