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Unit 7Multi-Level Gate Circuits /

NAND and NOR GatesKu-Yaw Chang

canseco@mail.dyu.edu.tw Assistant Professor, Department of

Computer Science and Information EngineeringDa-Yeh University

mailto:canseco@mail.dyu.edu.twmailto:canseco@mail.dyu.edu.tw

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Contents7.1 Multi-Level Gate Circuits7.2 NAND and NOR Gates7.3 Design of Two-Level Circuits Using NAND

and NOR Gates7.4 Design of Multi-Level NAND and NOR Gate

Circuits7.5 Circuit Conversion Using Alternative Gate

Symbols7.6 Design of Two-Level, Multiple-Output

Circuits7.7 Multiple-Output NAND and NOR Circuits

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7.4 Design of Multi-Level NAND-and NOR-Gates Circuits

Multi-Level NAND-gate circuitsSimplify the switching function to be realized.Design a multi-level circuit of AND and OR gates. The

output gate must be OR. AND-gate outputs cannot beused as AND-gate inputs; OR-gate outputs cannot beused as OR-gate inputs.Number the levels starting with the output gate as

level 1. Replace all gates with NAND gates, leavingall interconnections between unchanged. Leave theinputs to levels 2, 4, 6, unchanged. Invert anyliterals which appear as inputs to levels 1, 3, 5,

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Multi-Level NAND-gate circuits

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Contents7.1 Multi-Level Gate Circuits7.2 NAND and NOR Gates7.3 Design of Two-Level Circuits Using NAND

and NOR Gates7.4 Design of Multi-Level NAND and NOR Gate

Circuits7.5 Circuit Conversion Using Alternative Gate

Symbols7.6 Design of Two-Level, Multiple-Output

Circuits7.7 Multiple-Output NAND and NOR Circuits

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Alternative Gate Symbols

AND, OR, NAND, and NOR gatesBased on DeMorgans law

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Alternative Gate Symbols

Why alternative symbols?Facilitate the analysis and design of NAND and NORgate circuits

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NAND Gate Circuit Conversion

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Conversion to NOR Gates

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Conversion of AND-OR Circuit toNAND Gates

Convert all AND gates to NAND gates Adding an inversion bubble at the output

Convert all OR gates to NAND gates Adding inversion bubbles at the inputs

An inverted output drives an inverted inputNo further action

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Conversion of AND-OR Circuit toNAND Gates

A non-inverted gate output drives aninverted gate input or vice versa

Insert an inverter

A variable drives an inverted inputComplement the variable

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Conversion of AND-OR Circuit toNAND Gates

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Contents7.1 Multi-Level Gate Circuits7.2 NAND and NOR Gates7.3 Design of Two-Level Circuits Using NAND

and NOR Gates

7.4 Design of Multi-Level NAND and NOR GateCircuits7.5 Circuit Conversion Using Alternative Gate

Symbols7.6 Design of Two-Level, Multiple-Output

Circuits7.7 Multiple-Output NAND and NOR Circuits

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7.6 Design of Two-Level,Multiple-Output Circuits

The realization of several functions of thesame variables

A more economical realization

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Multi-Output Function

Given Functions

F1(A, B, C, D) = m(11, 12, 13, 14, 15)

F2(A, B, C, D) = m(3, 7, 11, 12, 13, 15)

F3(A, B, C, D) = m(3, 7, 12, 13, 14, 15)

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Separate Realizations

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Multiple-Output Simplification

F1 = AB + ACD

F2 = ABC + CD

F3 = ACD + AB

AB: F 1 and F 3

CD (F 2) can be replaced by ACD + ACD F2 = ABC + ACD + ACD

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Comparison

Gates GateInputs

Level

SeparateRealization 9 21 2

Multiple-OutputRealization

7 18 2

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Multiple-Output Simplification

If several solutions are availableTry to minimize the total number of gatesrequiredChoose the one with minimum gates inputs

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Contents7.1 Multi-Level Gate Circuits7.2 NAND and NOR Gates7.3 Design of Two-Level Circuits Using NAND

and NOR Gates7.4 Design of Multi-Level NAND and NOR Gate

Circuits7.5 Circuit Conversion Using Alternative Gate

Symbols

7.6 Design of Two-Level, Multiple-OutputCircuits7.7 Multiple-Output NAND and NOR Circuits

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7.7 Multiple-Output NAND andNOR Circuits

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Homework #1

1. 7.12. 7.3

3. 7.44. 7.85. 7.10

6. 7.177. 7.198. 7.209. 7.2510. 7.26

Paper Submission, due on March 22, 2004.Late submission will not be accepted.