218L8F08a - ESE218 Lecture 8 Dont cares Algorithmic...

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9/25/08 ESE218 Fall 2008 Lecture 8 1 ESE218 Lecture 8 Don’t cares. Algorithmic minimization. Outline ± Incompletely specified functions (functions with don’t cares) ² Prime Implicants and Essential Prime Implicants ² Examples, BCD to 2421 code converter ± Quine-McCluskey method ± Iterated consensus ± Summary
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9/25/08 ESE218 Fall 2008 Lecture 8 2 Incompletely specified functions 1 1 1 × 1 BC 01 00 11 10 A 0 1 F(A,B,C) = Σ (2, 5, 6, 7) + d (1) PI: 1) 2) 3) 4) EPI Solutions 1: 2: 3: 4: Minimal solution Don’t cares do not make P.I. essential!
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9/25/08 ESE218 Fall 2008 Lecture 8 3 Binary–to-2421 code converter: the truth table B i n a r y -to- 2 4 2 1 1 1 1 1 1 0 0 1 9 × × × × 0 1 0 1 A × × × × 1 1 0 1 B × × × × 0 0 1 1 C × × × × 1 0 1 1 D × × × × 0 1 1 1 E × × × × 1 1 1 1 F 0 1 1 1 0 0 0 1 8 1 0 1 1 1 1 1 0 7 0 0 1 1 0 1 1 0 6 1 1 0 1 1 0 1 0 5 0 0 1 0 0 0 1 0 4 1 1 0 0 1 1 0 0 3 0 1 0 0 0 1 0 0 2 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 F 0 F 1 F 2 F 3 D C B A # Outputs = don’t cares for input codes exceeding 9 Four different functions: F3 (A,B,C,D) F2 (A,B,C,D) F1 (A,B,C,D) F0 (A,B,C,D)
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9/25/08 ESE218 Fall 2008 Lecture 8 4 Incompletely-specified functions F3, F2 Binary-to-2421 code converter: F 3 = A + BD + BC X X X X X X 1 1 1 1 1 CD 01 00 11 10 AB 00 01 11 10 X X X X X X 1 1 1 1 1 CD 01 00 11 10 AB 00 01 11 10 F 2 = A + BD’ + BC
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9/25/08
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This note was uploaded on 03/21/2010 for the course ESE 218 taught by Professor Donetsky during the Fall '08 term at SUNY Stony Brook.

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218L8F08a - ESE218 Lecture 8 Dont cares Algorithmic...

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