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For a Karnaugh map of three or more variables deciding which side the variables go makes the solution easier to spot and simpler. But how do you know which side which variables go on.

eg. For variables x, y and z; You could have x and y as column headers and z as a row header or you could have y and z as column headers and x as a row header which would give two different tables

Tristan Warren
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  • Honestly, I can't imagine that any method for figuring out which arrangement makes the solution easiest to spot is going to be any easier than simply spotting solutions even in harder-to-spot cases. (Also, I'm sure it's subjective. For me, there's not a big difference between having x and y as column headers vs. having y and z as column headers; what makes a K-map easier or harder for me is whether the solutions "wrap around", which has more to do with whether x precedes y or vice versa.) – ruakh Jan 09 '17 at 01:21
  • Mine looks like this https://imgur.com/a/uHYLfPX – A P Feb 07 '22 at 10:26

2 Answers2

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For maps with up to four variables, it is a matter of taste, which variable is put at which side. However, Mahoney maps as extension of Karnaugh maps for five and more variables do require a certain ordering along the side.

Expression for the following examples:

abcd!e + abc!de

Five-input Mahoney map:

enter image description here

Equivalent Karnaugh map:

            de                     de
      00  01  11  10         00  01  11  10
 abc +---+---+---+---+  abc +---+---+---+---+
 000 | 0 | 0 | 0 | 0 |  001 | 0 | 0 | 0 | 0 |
     +---+---+---+---+      +---+---+---+---+
 010 | 0 | 0 | 0 | 0 |  011 | 0 | 0 | 0 | 0 |
     +---+---+---+---+      +---+---+---+---+
 110 | 0 | 0 | 0 | 0 |  111 | 0 | 1 | 0 | 1 |
     +---+---+---+---+      +---+---+---+---+
 100 | 0 | 0 | 0 | 0 |  101 | 0 | 0 | 0 | 0 |
     +---+---+---+---+      +---+---+---+---+

It is always possible to swap variables as shown here:

enter image description here

           de                     de
      00  01  11  10         00  01  11  10
 abc +---+---+---+---+  abc +---+---+---+---+
 000 | 0 | 0 | 0 | 0 |  001 | 0 | 0 | 0 | 0 |
     +---+---+---+---+      +---+---+---+---+
 010 | 0 | 0 | 0 | 0 |  011 | 0 | 0 | 0 | 0 |
     +---+---+---+---+      +---+---+---+---+
 110 | 0 | 0 | 0 | 0 |  111 | 0 | 1 | 0 | 1 |
     +---+---+---+---+      +---+---+---+---+
 100 | 0 | 0 | 0 | 0 |  101 | 0 | 0 | 0 | 0 |
     +---+---+---+---+      +---+---+---+---+

Here you can find a nice online-tool to draw and simplify Karnaugh-Veitch/Mahoney maps.

Axel Kemper
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The best approach to deciding which variables go to which side of the K-map is by first identifying the most significant variables and then putting that on the rows. For example;

For variables X, Y, and Z, if you regard X and the MSB and Z as the least, then you use X as the row header and YZ as the column header.

Kimutai Ngetich
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