Ch03a-CombinationalDesign

# Ch03a-CombinationalDesign - 6 12 13 15 14 8 9 11 10 K-Map...

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Combinational Logic Design ECE 25 Chapter 3 ©Clark Guest 2009 ECE 25 Logic and Computer Design Topics The Design Process Decoders Encoders Multiplexers 2 ©Clark Guest 2009 ECE 25 Logic and Computer Design The Design Process Specifcation Fully speci±y the circuit you are building: inputs, outputs, ±unctional relationships, speed, cost goals, etc. Formulation Develop the algebraic expressions and/or truth-tables that defne the relationships Optimization Apply two-level and multi-level optimization. Draw logic diagram. Technology Mapping Adapt the logic diagram to available implementation technology Verifcation Veri±y that the design satisfes the specifcation 3 ©Clark Guest 2009 ECE 25 Logic and Computer Design Example Design: BCD to Seven-Segment Specifcation: 4 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 Formulation: A B C D a b c d e ± g 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 1 1 1 1 0 0 1 0 1 0 0 0 1 1 0 0 1 1 0 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 a b c d e ± g

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©Clark Guest 2009 ECE 25 Logic and Computer Design BCD to Seven-Segment: Optimization AB\CD 00 01 11 10 00 01 11 10 1 0 1 1 0 1 1 1 0 0 0 0 1 1 0 0 0 1 3 2 4 5 7
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Unformatted text preview: 6 12 13 15 14 8 9 11 10 K-Map for “a” Segment a = A’C+A’B’D’+A’BD+AB’C’ AB\CD 00 01 11 10 00 01 11 10 1 1 1 1 1 1 X X X X 1 1 X X 1 3 2 4 5 7 6 12 13 15 14 8 9 11 10 K-Map using “Don’t Cares” a = C+AB’+BD+B’D’ Repeat for all segments b through g ©Clark Guest 2009 ECE 25 Logic and Computer Design Technology Mapping a = C+AB’+BD+B’D’ A B C D AND-OR Mapping A B C D NAND Mapping A B C D NOR Mapping a = C+AB’+BD+B’D’ = (C’•(AB’)’•(BD)’•(B’D’)’)’ a = C+AB’+BD+B’D’ = (C’•(AB’)’•(BD)’•(B’D’)’)’ = (C’•(A’+B)•(B’+D’)•(B+D))’ = (C+(A’+B)’+(B’+D’)’+(B+D)’)...
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Ch03a-CombinationalDesign - 6 12 13 15 14 8 9 11 10 K-Map...

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