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SFU - CMPT 150 - Practice Exams - Solutions - Final (1041)

SFU - CMPT 150 - Practice Exams - Solutions - Final (1041)...

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CMPT 150 SAMPLE FINAL EXAMINATION Time: 3 Hours SPRING 5 Questions CLOSED BOOK Name:_________________________________ 1. A combinational circuit for a Boolean function f(a,b,c,d) is defined by the following Karnaugh map: f 0 0 0 1 0 1 1 0 1 0 1 1 X X X X c,d a,b 10 11 01 00 10 11 01 00 a. Express f as a minimal sum-of-products. (2 marks) ANSWER: f(a,b,c,d) = a’d’ + b’c + b’d’ b. Express f as a minimal product-of-sums. (2 marks) ANSWER: f(a,b,c,d) = (c + d’)(b’ + d’)(a’ + b’) c. Express f as a sum of minterms using Σ -notation. (2 marks) ANSWER: f(a,b,c,d) = Σ m (2,3,4,6,8,11) + Σ d(0,5,10,15) d. Express f as a product of maxterms using Π -notation. (2 marks) ANSWER: f(a,b,c,d) = Π M (1,7,9,12,13,14) + Π d(0,5,10,15)

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1 Name:_________________________________ e. Express the complement of f as a product of maxterms in Π -notation. (2 marks) ANSWER: f(a,b,c,d) = Π M (2,3,4,6,8,11) + Π d(0,5,10,15) f. Give the dual of the complement of f , expressed as a sum-of-minterms in Σ -notation. (3 marks) ANSWER: f’(a,b,c,d) = Σ m (1,7,9,12,13,14) + Σ d(0,5,10,15) = a’b’c’d + a’bcd + ab’c’d + abc’d’ + abc’d + abcd’ f’ (a,b,c,d) = dual (a’+b’+c’+d)(a’+b+c+d)(a+b’+c’+d) *(a+b+c’+d’)(a+b+c’+d)(a+b+c+d’) g. How is the result in part (f) related to the original function f , other than that it is the dual of the complement? That is, what conclusion might you draw about a function and the dual of its complement? (1 mark) . ANSWER: f’ (a,b,c,d) = dual Π M (1,2,3,6,8,14) + Π d(0,5,10,15) f(a,b,c,d) = Σ m (2,3,4,6,8,11) + Σ d(0,5,10,15) f(a’b’c’d’) = Σ m (13,12,11,9,7,4) + Π d(0,5,10,15) = Π M (1,2,3,6,8,14) + Π d(0,5,10,15) Therefore f(a’b’c’d’) = f’ (a,b,c,d) dual
2 Name:_________________________________ 2. The following state diagram defines the behavior of a sequential machine. This machine processes a binary integer of arbitrary length, one bit at a time, with the least significant bit being the first bit supplied.

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SFU - CMPT 150 - Practice Exams - Solutions - Final (1041)...

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