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The Four Input KMap student version

# The Four Input KMap student version - EC262 Topic 6 The...

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1 EC262 Topic 6: The Four-Input Karnaugh Map The extension of three-input K-maps to four-input K-maps is quite straightforward. Four-Input Karnaugh Maps A digital logic circuit with four separate inputs (let’s call them A , B , C and D ) has 4 2 16 = possible input combinations: 0000, 0001, …, 1110, 1111. In other words, the truth table for this circuit will have 16 lines. Each of these possible input combinations represents a minterm. For instance, the input combination 0101 represents the minterm : There will, of course, be an output for each of the sixteen possible input minterm combinations. The K-map for a four-input problem is a table where the rows and columns (together) account for all possible inputs to logic circuit. The outputs are displayed in a four-input K-map that is organized as follows: AB CD 00 01 11 10 00 01 11 10 Note that the rows and columns are arranged in the order from left to right (and from top to bottom) as: 00 01 11 10 . Take a moment to memorize this order. Note that the order is NOT 00 01 10 11 . Exactly as with the three-input K-map, the entry in each table cell of the four-input K-map corresponds to the output for the inputs specified by the row and column. Within each of the sixteen squares of the K-map, we place the output (0 or 1) that corresponds to the input minterm. From Introduction to Logic Design , Alan Marcovitz, McGraw Hill, 2010 Example. Suppose a digital logic circuit with three inputs ( x , y , z ) has the following Boolean expression:

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