Karnaugh map: mirroring tables

designkarnaugh map

When creating a map for n variables, we have to do (n-1) mirrorings. I wonder, why are the variables assigned in the way you see it on the picture. How do I know, when expanding a map, where to place the next added variable?
Could you please help to understand this?

PS: the picture is from the book "Technische Informatik" by Hoffmann.
enter image description here

Best Answer

That depends on where you place your variables in the gray code running along the edges. If you write out the graycode you will see that every square contains the combined graycode from the horizontal and vertical edge (with x_5x_4x_3x_2x_1 in the the right order of course) interpreted as a binary number.

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