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I want to simply the following expression:

(NOT A AND NOT B AND NOT C) OR (NOT A AND B) OR (A AND B AND NOT C) OR (A AND C)

I created a truth table first, then a K map from the truth table. (See below.)

As far as I can tell, the simplest expression I can derive purely from the K-map is:

(A AND NOT C) OR B OR (A AND C)

But I can reduce this further with Boolean algebra to:

A OR B

Is it fair to say that a K-map will not always give the best possible solution?

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    \$\begingroup\$ Something is wrong here, your truth table doesn't match what you're saying: In the first row A=B=C=0 and F=1, but with A OR B it should be F=0. (Similar problem in the fifth row.) \$\endgroup\$
    – Michael
    Commented Aug 13, 2016 at 10:51
  • \$\begingroup\$ Your derived expression is incorrect. It's (!A*!C)+B+(A*C) \$\endgroup\$
    – W5VO
    Commented Aug 13, 2016 at 10:56
  • \$\begingroup\$ @Michael The truth table and k map look right to me. \$\endgroup\$
    – W5VO
    Commented Aug 13, 2016 at 11:05
  • \$\begingroup\$ When I look at the K-map again, I can see the top left group of two ones represents (NOT A AND NOT C). So the final expression is indeed (NOT A AND NOT C) OR B OR (A AND C) and this agrees with Woolfram Alpha's calculator. I think my truth table does represent the original expression and the K-map reflects the truth table. I interpreted the K-map wrongly. Sloppy of me. I feel silly now. \$\endgroup\$
    – Drummy
    Commented Aug 13, 2016 at 11:57

1 Answer 1

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Karnaugh map are a very good way to simplify logic expressions. However, more than four variables can get a bit tedious for us humans to do.

Moreover, its very difficult to spot something called "Static Hazards" if you tread down the algebraic simplification path. Designs that are Static Hazard free are very important in digital design and Karnaugh maps can be used to avoid them.

Karnaugh maps will always get you the simplest expression as long as you form the largest group possible even if that means looping(including) ones you have already accounted for.

With regards to your observation, it is wrong. You cannot simplify this to A OR B, look at line one on your Truth Table.....

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