K2 Choosing Prime Implicants

# K2 Choosing Prime Implicants - When Karnaugh Maps Attack I...

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When Karnaugh Maps Attack I use this function to motivate a demonstration of the Quine-McCluskey algorithm wherein a designer reaches the point where he can’t choose any more prime implicants, either because none are essential or because none possess a quality called dominance . (We’ve already discussed the concept without using the term. I’ll have more to say about it later.) As a basis for comparison, we can observe the development of this same example using a Karnaugh map. ( 29 ( 29 31 , 30 , 29 , 28 , 26 , 25 , 24 , 23 , 22 , 19 , 18 , 17 , 14 , 12 , 11 , 9 , 7 , 6 , 3 E D, C, B, A, = m f Here’s the mapped function: DE 00 01 11 10 00 01 11 10 BC 00 0 0 1 0 00 0 1 1 1 01 0 0 1 1 01 0 0 1 1 11 1 0 0 1 11 1 1 1 1 10 0 1 1 0 10 1 1 0 1 A = 0 A = 1 This function has 15 prime implicants. The easiest way to see all of them is to highlight them on different maps: DE DE DE 00 01 11 10 00 01 11 10 00 01 11 10 00 01 11 10 00 01 11 10 00 01 11 10 BC 00 0 0 1 0 00 0 1 1 1 BC 00 0 0 1 0 00 0 1 1 1 BC 00 0 0 1 0 00 0 1 1 1 01 0 0 1 1 01 0 0 1 1 01 0 0 1 1 01 0 0 1 1 01 0 0 1 1 01 0 0 1 1 11 1 0 0 1 11 1 1 1 1 11 1 0 0 1 11 1 1 1 1 11 1 0 0 1 11 1 1 1 1 10 0 1 1 0 10 1 1 0 1 10 0 1 1 0 10 1 1 0 1 10 0 1 1 0 10 1 1 0 1 A = 0 A = 1 A = 0 A = 1 A = 0 A = 1 ABC (28,29,30,31) ABD′ (24,25,28,29) AB′D (18,19,22,23) DE DE DE 00 01 11 10 00 01 11 10 00 01 11 10 00 01 11 10 00 01 11 10 00 01 11 10 BC 00 0 0 1 0 00 0 1 1 1 BC 00 0 0 1 0 00 0 1 1 1 BC 00 0 0 1 0 00 0 1 1 1 01 0 0 1 1 01 0 0 1 1 01 0 0 1 1 01 0 0 1 1 01 0 0 1 1 01 0 0 1 1 11 1 0 0 1 11 1 1 1 1 11 1 0 0 1 11 1 1 1 1 11 1 0 0 1 11 1 1 1 1 10 0 1 1 0 10 1 1 0 1 10 0 1 1 0 10 1 1 0 1 10 0 1 1 0 10 1 1 0 1 A = 0 A = 1 A = 0 A = 1 A = 0 A = 1 ABE′ (24,26,28,30) ACD (22,23,30,31) ADE′ (18,22,26,30)

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DE DE DE 00 01 11 10 00 01 11 10 00 01 11 10 00 01 11 10 00 01 11 10 00 01 11 10 BC 00 0 0 1 0 00 0 1 1 1 BC 00 0 0 1 0 00 0 1 1 1 BC 00 0 0 1 0 00 0 1 1 1 01 0 0 1 1 01 0 0 1 1 01 0 0 1 1 01 0 0 1 1 01 0 0 1 1 01 0 0 1 1 11 1 0 0 1 11 1 1 1 1 11 1 0 0 1 11 1 1 1 1 11 1 0 0 1 11 1 1 1 1 10 0 1 1 0 10 1 1 0 1 10 0 1 1 0 10 1 1 0 1 10 0 1 1 0 10 1 1 0 1 A = 0 A = 1 A = 0 A = 1 A = 0 A = 1 B′CD (6,7,22,23) BCE′ (12,14,28,30) B′DE (3,7,19,23) DE DE DE 00 01 11 10 00 01 11 10 00 01 11 10 00 01 11 10 00 01 11 10 00 01 11 10 BC 00 0 0 1 0 00 0 1 1 1 BC 00 0 0 1 0 00 0 1 1 1 BC 00 0 0 1 0 00 0 1 1 1 01 0 0 1 1 01 0 0 1 1 01 0 0 1 1 01 0 0 1 1 01 0 0 1 1 01 0 0 1 1 11 1 0 0 1 11 1 1 1
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## This note was uploaded on 01/17/2011 for the course ECE 3504 at Virginia Tech.

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K2 Choosing Prime Implicants - When Karnaugh Maps Attack I...

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