hw04_sol

hw04_sol - LSU EE 2720-2 Homework 4 Solution Due: 2...

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LSU EE 2720-2 Homework 4 Solution Due: 2 November 2011 Problem 1: Consider the following logic function in canoncial form: a,b,c,d m (0 , 2 , 5 , 8 , 10 , 12 , 13). ( a ) Draw a truth table for this logic function. SOLUTION: row a b c d ! f -------------+---- 0 0 0 0 0 ! 1 1 0 0 0 1 ! 0 2 0 0 1 0 ! 1 3 0 0 1 1 ! 0 4 0 1 0 0 ! 0 5 0 1 0 1 ! 1 6 0 1 1 0 ! 0 7 0 1 1 1 ! 0 8 1 0 0 0 ! 1 9 1 0 0 1 ! 0 10 1 0 1 0 ! 1 11 1 0 1 1 ! 0 12 1 1 0 0 ! 1 13 1 1 0 1 ! 1 14 1 1 1 0 ! 0 15 1 1 1 1 ! 0 ( b ) Draw a logic circuit for this function. Do not simplify. Diagram appears below. The and gates are labeled with minterm numbers. a b c d 0 2 5 8 10 12 13 ( c ) Draw a Karnaugh map for the logic function. Solution appears below, the prime implicants are circled. 1
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ab c d 00 00 0 1 10 11 01 11 10 1 1 1 1 1 1 1 b'd' bc'd abc' ac'd' ( d ) List the prime implicants. As shown in the Karnaugh map above, the prime implicants are: b d , abc , bc d , and ac d . ( e ) List the essential prime implicants. The essential prime implicants are b d (because of minterms 0, 2, and 10), and bc d (because of minterm 5). ( f ) List all of the minimum cost sum-of-product expressions.
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hw04_sol - LSU EE 2720-2 Homework 4 Solution Due: 2...

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