hw09_SLN

# hw09_SLN - ECE 211 HW 9 SOLUTIONS p 1 of 10...

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ECE 211 HW 9 SOLUTIONS p 1 of 10 //home/vdimitrov/4620/b24a07fb67d6cb192b5e9abb95e99b486765c312.doc HW Set 9 – SOLUTIONS 1. Determine the PLA size needed to realize the four functions F1 (A,B,C,D) = Σ m ( 2, 5, 6, 10, 11, 13) F2 (A,B,C,D) = Σ m ( 5, 9, 11, 13) F3 (A B,C,D) = Σ m ( 5, 7, 8, 10) F4 (A B,C,D) = Σ m ( 2, 4, 5, 6) Base your realization on summing minterms. Solution: F1 (A,B,C,D) = Σ m ( 2, 5, 6, 10, 11, 13 ) F2 (A,B,C,D) = Σ m ( 5, 9, 11, 13 ) F3 (A B,C,D) = Σ m ( 5, 7, 8, 10 ) F4 (A B,C,D) = Σ m ( 2, 4, 5, 6 ) We need ten minterms. The PLA size is 4 × 10 × 4 .

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ECE 211 HW 9 SOLUTIONS p 2 of 10 2. Your friendly PLA vendor sales rep claims that his 839 PLA is capable of realizing any six functions, each a function of the same 5 variables: F1( A, B, C, D, E ) F2( A, B, C, D, E ) F3( A, B, C, D, E ) F4( A, B, C, D, E ) F5( A, B, C, D, E ) F6( A, B, C, D, E ) He boasts that the functions can contain any number of minterms. Do you agree, or do you start looking for another PLA vendor? Solution: With 5 variables there are 2 5 = 32 minterms. The 839 PLA has 32 product lines so we can realize all the minterms on the product lines. With all minterms available, we can realize any function of 5 variables. The PLA has 6 outputs, so we can realize any six functions of A, B, C, D, E.
ECE 211 HW 9 SOLUTIONS p 3 of 10 3. For the functions F1(A,B,C,D) = Σ m( 0, 4, 5, 11, 13, 15 ) F2(A,B,C,D) = Σ m( 0, 1, 5, 7, 15 ) F3(A,B,C,D) = Σ m( 0, 4, 5, 7, 13, 15 ) F4(A,B,C,D) = Σ m( 4, 5, 9, 11, 13 ) (a) How many PLA product lines do you need if you realize minterms on the product lines? (b) Using Karnaugh maps, write minimal sum-of-product expressions for the functions. (c) How many PLA product lines do you need if you realize your minimal expressions? Solution: (a) F1(A,B,C,D) = Σ m( 0, 4, 5, 11, 13, 15 ) F2(A,B,C,D) = Σ m( 0, 1, 5, 7, 15 ) F3(A,B,C,D) = Σ m( 0, 4, 5, 7, 13, 15 ) F4(A,B,C,D) = Σ m( 4, 5, 9, 11, 13 ) There are 9 distinct minterms; we need 9 product lines . (b) Minimal sum-of-product expressions:

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ECE 211 HW 9 SOLUTIONS p 4 of 10 ( 3 b ) Alternate Solution: Using a different minimal expression for F4.
ECE 211 HW 9 SOLUTIONS p 5 of 10 (3.) CUPL results: Products = 4 + 3 + 4 + 3 – 7 = 7 =============================================================================== Expanded Product Terms =============================================================================== F1 =>

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## This homework help was uploaded on 04/17/2008 for the course ECE 211 taught by Professor Nestor during the Fall '07 term at Lafayette.

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hw09_SLN - ECE 211 HW 9 SOLUTIONS p 1 of 10...

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