Lecture 3b- Logic Gate Implementation

# Lecture 3b- Logic Gate Implementation - ELEC151 Spring 2011...

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ELEC151 Spring 2011 – L. Yobas Lecture 3b – 1 Lecture 3b Gate Level Implementation ELEC151 Digital Circuits and Systems Spring 2011 Instructor: Levent Yobas

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ELEC151 Spring 2011 – L. Yobas Lecture 3b – 2 Lecture Overview Implementations Using AND-OR, OR- AND Using NAND-NAND, NOR-NOR Multi-level circuits using NAND XOR gates Programmable Logic Array (PLA) Programmable Array Logic (PAL) Reading assignment: Chapter 3.7 to 3.9, Chapter 7.6 and 7.7
ELEC151 Spring 2011 – L. Yobas Lecture 3b – 3 NAND and NOR Implementations AND, OR and NOT are primitive gates for Boolean expressions NAND and NOR gates are basic integrated circuits NAND and NOR gates can be expressed by primitive gates We have shown in Lecture 2 that NAND = AND/NOT = NOT/OR NOR = OR/NOT = NOT/AND

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ELEC151 Spring 2011 – L. Yobas Lecture 3b – 4 NAND and NOR Implementations Similarly, All primitive gates can be expressed by NAND or NOR gates NOT 1-input NAND or NOR gate AND = NAND-NOT = NOT-NOR OR= NOT-NAND = NOR-NOT Every logic expression can be implemented with NAND gates only! (or with NOR gates only)
ELEC151 Spring 2011 – L. Yobas Lecture 3b – 5 NAND and NOR Implementations There are two meaningful two-level Boolean expressions Sum of Minterms: (NOT-) AND-OR Product of Maxterms: (NOT-) OR-AND How about AND-AND ? Or OR-OR ? In one-level Boolean expressions AND = NAND-NOT = NOT-NOR OR = NOT-NAND = NOR-NOT In two-level Boolean expressions AND-OR = (NAND-NOT)-(NOT-NAND) = NAND-NAND OR-AND = (NOR-NOT)-(NOT-NOR) = NOR-NOR In multi-level Boolean expressions Follow a similar approach

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ELEC151 Spring 2011 – L. Yobas Lecture 3b – 6 AND-OR to NAND-NAND Conversions F = [(A•B)' (C•D)']‘ = [(A' + B') (C' + D')]‘ = [(A' + B')' + (C' + D')'] = (A • B) + (C • D)
ELEC151 Spring 2011 – L. Yobas Lecture 3b – 7 OR-AND (Product of Sums) to NAND Gates Conversion The results is: invert inputs -> NAND-NAND (AND-OR) -> invert output i.e. the same as - minimizing F’ to SoP form, - implementing using AND-OR (NAND-NAND), - and inverting the output.

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ELEC151 Spring 2011 – L. Yobas Lecture 3b – 8 OR-AND to NOR-NOR Conversions AND (B) A B C D OR AND (A) A B C D NOR NOR NOR (C) A B C D AND AND AND F = [(A + B)' + (C + D)']' = [(A' • B') + (C' • D')]' = (A' • B')' • (C' • D')' = (A + B) • (C + D)
Lecture 3b – 9 AND-OR to NOR Gates ? (A)

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Lecture 3b- Logic Gate Implementation - ELEC151 Spring 2011...

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