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SP10-hw3-sol

# SP10-hw3-sol - UNIVERSITY OF CALIFORNIADAVIS DEPARTMENT OF...

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UC Davis 1 Hussain Al-Asaad U NIVERSITY OF C ALIFORNIA —D AVIS D EPARTMENT OF E LECTRICAL & C OMPUTER E NGINEERING EEC180A—D IGITAL S YSTEMS I Spring 20 10 P ROBLEM S ET 3—S OLUTION 1. P ROBLEM 3.6 ( PART B ) 2. P ROBLEM 3.9 ( PART E ) fABCD ,,, () m 157891 31 5 ,,,,, , d 41 21 4 ,, + = Implication Table Column I Column II Column III 0001 D 0-01 D --01 * 0100 D -001 D -10- * 1000 D 010- D 1-0- * -100 D 0101 D 100- D -1-1 * 1001 D 1-00 D 11-- * 1100 D 01-1 D 0111 D -101 D 1101 D 1-01 D 1110 D 110- D 11-0 D 1111 D -111 D 11-1 D 111- D Prime Implicant Chart 3 1 5 1,5,9,13 (--01) X X X X 5,13 (-10-) X X 8,9,13 (1-0-) X X X 5,7,13,15 (-1-1) X X X X 13,15 (11--) X X It is obvious from the prime implicant chart that there are three essential prime implicants: --01 , 1-0- , and -1-1 . These essential prime implicants cover all the minterms of the function. So, the minimum sum of products expression for the function is: CD AC BD ++ = C A A B F C A A B F

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UC Davis 2 Hussain Al-Asaad 3. P ROBLEM 3.18 ( PART D ) Implement the function in a hazard free manner. Using the Karnaugh map, the minimum product of sums for F is . To eliminate static 0-hazards from a product of sums implementation, we need to include the redundant prime
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SP10-hw3-sol - UNIVERSITY OF CALIFORNIADAVIS DEPARTMENT OF...

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