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RF Cascade Workbook 2005 - RF Cafe
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About RF Cafe

Kirt Blattenberger - RF Cafe WebmasterCopyright
1996 - 2016
Webmaster:
Kirt Blattenberger,
 BSEE - KB3UON

RF Cafe began life in 1996 as "RF Tools" in an AOL screen name web space totaling 2 MB. Its primary purpose was to provide me with ready access to commonly needed formulas and reference material while performing my work as an RF system and circuit design engineer. The Internet was still largely an unknown entity at the time and not much was available in the form of WYSIWYG ...

All trademarks, copyrights, patents, and other rights of ownership to images and text used on the RF Cafe website are hereby acknowledged.

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Karnaugh Maps / Tables

The Karnaugh map, also known as a Veitch diagram (KV-map or K-map for short), is a tool to facilitate the simplification of Boolean algebra integrated circuit expressions. The Karnaugh map reduces the need for extensive calculations by taking advantage of human pattern-recognition and permitting the rapid identification and elimination of potential race hazards.

The Karnaugh map was invented in 1952 by Edward W. Veitch. It was further developed in 1953 by Maurice Karnaugh, a physicist at Bell Labs, to help simplify digital electronic circuits.

In a Karnaugh map the boolean variables are transferred (generally from a truth table) and ordered according to the principles of Gray code in which only one variable changes in between squares. Once the table is generated and the output possibilities are transcribed, the data is arranged into the largest even group possible and the minterm is generated through the axiom laws of boolean algebra. - Wikipedia

Karnaugh Map (also known as the Veitch Diagram) reduction was developed as a graphic method of minimizing Boolean function. The 4-variable Karnaugh Map reduction shown here applies to any size map.

Example 4-Variable Map Problem
     4-Variable Karnaugh Map - RF Cafe

F(w,x,y,z) = ∑(0,1,2,4,5,6,8,9,12,13,14)                = y+w·z+x·z Minterms must be boxed in the smallest number of groups which results in all minterms being enclosed.
Generic 4-Variable Map
    Generic 4-Variable Karnaugh Map - RF Cafe

Note that w,x,y,z terms (and their compliments) are arranged in positions corresponding to the axis labels. One unique minterm exists in each square.
Generic 2-Variable Map
2-Variable Karnaugh Map - RF Cafe
Generic 3-Variable Map
     3-Variable Karnaugh Map - RF Cafe