Karnaugh Veitch Maps (KV Diagrams)

A guide to Karnaugh-Veitch maps and their usage

This guide has been moved to the official Turing Complete wiki

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Click here to visit this guide on the official wiki[turingcomplete.wiki]

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What is this guide about

A Karnaugh-Veitch map (aka K-map or KV diagram) is a modified truth table which allows techniques to build very simple circuits for any combination of 4 input variables.

[skilz80]

A tip in understanding the power and usefulness of Karnaugh Maps. They help to derive the boolean expression(s) Sums of Products, Product of Sums that are required in reducing a given truth table by removing all redundancies from the original truth table.

Within Boolean Algebra OR relates to Addition and AND relates to Multiplication. I'll be using ! to represent NOT before a given variable. Now consider the following expressions:

(AB) + (B!C) + (CD) read as (A AND B) OR (B AND NOT C) OR (C AND D)

This is a Sum of Products - AND your Inputs take their results and OR them as your output.

(A+C)(!B+C)(!A+D) read as (A OR C) AND (NOT B OR C) AND (NOT A OR D)

This is a Product of Sums. OR your inputs take their results and AND them as your output.

Now using core principles within Boolean Algebra such as DeMorgan's Law you can simplify your derived expression(s) to their simplest of forms thus giving you the smallest and most efficient logical diagram / circuit. Hope this helps.

[JSRagman]

Thank you. I had forgotten how to do this and was searching for my old books when I saw your guide.

I agree with Quadrivial. This would be a very useful manual page in the game. Maybe it is... I've only just started.

[CyBay]

Very instructive. Some details are far more in depth than other new and popular overviews about k-maps. Appreciated

[Zaxabock]

K-maps are cool but I think I prefer Quine-McCluskey method

[Quadrivial]

They should build something like this into the game. If you didn't go to college and study this in your DLD courses, it's not very intuitive. Adding a couple levels on the subject would be a great help to people who didn't have that luxury.