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So I'm trying to learn how to use Karnaugh maps. I've found what are the rules of simplification and how to apply them but every tutorial or lesson I find uses some generic function like "Here's how to do Karnaugh maps for three variables" and someone just does the truth table for A, B, C and then creates a map. But what if I wanted to simplify some specific function, say F=AB+A(B+C)? I can't just make a truth table for A, B, C and their sum because it's just not enough. So how should I solve it using Karnaugh maps? Should I make a "typical" truth table, i.e. for A, B, C, AB, B+C, A(B+C)? But how should this help me in drawing the map and simplyfing?

Could someone please tell me a little about it or point some direction? I'd really like to learn this but just can't get a grasp of it.

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  • \$\begingroup\$ "say F=AB+A(B+C)? I can't just make a truth table for A, B, C and their sum because it's just not enough." Why can't you make a truth table from the formula? Write down all possibilities for A, B and C followed by the resulting value for F. Make a table one column for each variable A,B,C,F and start filling it for ABC with all possibilities (there are eight), then for each line calculate F. \$\endgroup\$ – jippie Mar 24 '13 at 13:01
  • \$\begingroup\$ Oh, I believe I expressed myself wrong. As I write later: "Should I make a "typical" truth table, i.e. for A, B, C, AB, B+C, A(B+C)? But how should this help me in drawing the map and simplyfing?". I know I can do the truth table - what I don't know is how such a table should help me in drawing the final map. \$\endgroup\$ – Straightfw Mar 24 '13 at 13:16
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    \$\begingroup\$ The truth table for F would only need columns for A, B, C and F. You can add columns for AB, B+C and A(B+C) to aid in the intermediate determination of what the values of F will be for each ABC combination. But that may not be necessary if you can work out AB+A(B+C) in your head for each of the cases. I've shown an answer that shows the truth table to K-Map translation template for you to work with. \$\endgroup\$ – Michael Karas Mar 24 '13 at 14:39
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Just simply make a truth table that shows values of F for each of the combinations of A, B and C. Then transfer this information to the K-Map format table to do the minimization. enter image description here

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  • \$\begingroup\$ Oooh, I see. Thanks a lot! One more question, though - does it matter if I group the final K-map to "CB" and "A" axis or "C" and "AB"? Can I do it any way I want? \$\endgroup\$ – Straightfw Mar 24 '13 at 15:12
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    \$\begingroup\$ @Straightfw - You can group the K-Map as: AB/C, BA/C, AC/B, CA/B, BC/A or CB/A. You can pick as you see fit. Just make sure that when you transcribe from the truth table that you get the right values in the right places. Personally I find it best to group the K-Map as close to the truth table as possible to help to avoid mistakes. Also make sure that on the side of the K-Map with the two bit values that you order them properly as 00, 01, 11, and 10 so that mapping on the table works correctly. \$\endgroup\$ – Michael Karas Mar 24 '13 at 15:21
  • \$\begingroup\$ Great, thank you so much for the great explanation! I allowed myself to use your template, would you please care to take a look? I tried to minimize the example I threw in the comments section above (AB+A(B+C)): i.imgur.com/effxYfM.png \$\endgroup\$ – Straightfw Mar 24 '13 at 15:56
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    \$\begingroup\$ The solution in the image looks OK to me. \$\endgroup\$ – jippie Mar 24 '13 at 16:00

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