SP10-hw2-sol

SP10-hw2-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 2—S OLUTION 1. P ROBLEM 2.17 ( PART C ) = (Rule 6D) (Rule 8) (Rule 6) (Rule 5) (Rule 1D) (Rule 6D) (Rule 8) (Rule 6) (Rule 5) (Rule 1D) The original representation of the function has 8 literals. However, the simplified result has 1 literal, which corre- sponds to saving 7 literals. 2. P ROBLEM 2.25 ( PART C ) 3. P ROBLEM 2.27 ( PART C ) fXYZ ,, () YZ XYZ ++ = YZX YZ X X + + X + + 1 + + ZY + ZY Y + + Z 1 Z 00 01 11 10 CD AB 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 00 01 11 10 The representation of the function uses 2 literals. fABCD ,,, m 0246 = AD = 00 01 11 10 CD AB x 0 0 0 x 0 1 0 1 0 0 1 1 x 1 0 00 01 10 DA C + =
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UC Davis 2 Hussain Al-Asaad 4. P ROBLEM 2.45 c) If we think about using XOR gates, we can get the following expression: We can derive the above equation as follows: 00 01 11 10 CD AB 0 1 1 1 0 1 0 0 1 0 1 1 0 1 0 0 00 01 11 10 Input A B C D Output F 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 0 1 0 0 1 0 1 0 1 0 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 1 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 (a) Truth Table (d) No simplification possible using K-Map
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This note was uploaded on 04/25/2011 for the course EEC 180A taught by Professor Redinbo during the Spring '08 term at UC Davis.

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SP10-hw2-sol - UNIVERSITY OF CALIFORNIADAVIS DEPARTMENT OF...

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