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

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

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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) b. Express f as a minimal product-of-sums. (2 marks) c. Express f as a sum of minterms using Σ -notation. (2 marks) d. Express f as a product of maxterms using Π -notation. (2 marks)

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1 Name:_________________________________ e. Express the complement of f as a product of maxterms in Π -notation. (2 marks) f. Give the dual of the complement of f , expressed as a sum-of-minterms in Σ -notation. (3 marks) 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) .
2 Name:_________________________________ 2. The following state diagram defines the behavior of a sequential machine. This machine

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