Basic Logic Operationsand

Standard Logic Gates

(Lecture #1)

ECE 331 – Digital System Design

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What is an analog signal?

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Analog Signal

An analog signal is a signal that can take on a continuous range of values.

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Analog Signal

Most, if not all, physical (naturally occurring) quantities are analog values.

Time Temperature Pressure

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What is an digital signal?

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Digital Signal

An digital signal is a signal that can take on only discrete (specific) values.

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What is an binary signal?

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Binary Signal

An binary signal is a signal that can take on only two values.

Typically represented by 0 and 1.

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Can a binary number be used to represent an analog value?

What about accuracy (or is it precision)?

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Can a binary number be used to represent an digital value?

How many bits are required?

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Processing Physical Quantities

The analog signal (representing the physical quantity) must be sampled at specific instances in time.

The sampled values must be digitized. The digital value must be encoded in binary.

SampleandHold

ADC BinaryEncoder

analog sampled digital binary

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Basic Logic Operations

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AND

Definition: the output is true (1) iff both inputs are true (1).

F = A.B = AB = “A and B”Boolean expression

logical operator

A B A . B

0 0 0

0 1 0

1 0 0

1 1 1

Truth tableF

Symbol (aka. logic gate)

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OR

Definition: the output is true (1) if either or both inputs are true (1).

F = A+B = “A or B”Boolean expression

logical operator

A B A + B

0 0 0

0 1 1

1 0 1

1 1 1

Truth table

Symbol

F F

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NOT

Definition: the output is true (1) if the input is false (0).

F = A' = “ not A”Boolean expression

logical operator

A A'

0 1

1 0

Truth table

Symbol

A F = A'

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Order of Precedence

The order of precedence of the basic logic operations is defined as follows:

– NOT– AND– OR

The order of precedence can be modified by using parenthesis.

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Functionally Complete

The AND, OR, and NOT operations comprise a functionally complete set.

All logic functions can be expressed in terms of these logic operations.

All logic circuits can be realized using the associated logic gates.

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NAND

Definition: the output is false (0) iff both inputs are true (1).

F = (A.B)' = “not (A and B)”Boolean expression

A B (A . B)'

0 0 1

0 1 1

1 0 1

1 1 0

Truth tableF = (A.B)'

Symbolshorthand for inversion

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NOR

Definition: the output is false (0) if either or both inputs are true (1).

F = (A+B)' = “not (A or B)”Boolean expression

A B (A+B)'

0 0 1

0 1 0

1 0 0

1 1 0

Truth table

Symbol

F FFF = (A+B)'

shorthand for inversion

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XOR

Definition: the output is true (1) if either but not both inputs are true (1).

F = A xor BBoolean expression

A B A xor B

0 0 0

0 1 1

1 0 1

1 1 0Truth table

Symbol

logical operator

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XNOR (aka. Equivalence)

Definition: the output is false (0) if either but not both inputs are true (1).

F = A xnor BBoolean expression

A B A xnor B

0 0 1

0 1 0

1 0 0

1 1 1

Truth tableSymbol

logical operator

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Logic Circuits Logic circuits are realized through the

interconnection of logic gates. Each logic gate represents a logical operation.

This can be done using discrete components

Standard Logic Gates programmable devices

Read-only Memories (ROM) Programmable Logic Devices (PLD) Field Programmable Gate Arrays (FPGA)

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Standard Logic Gates

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Standard Logic Gates

Device Logic Gate

74xx08 Quad 2-input AND gate

74xx32 Quad 2-input OR gate

74xx04 Hex Inverter (NOT gate)

74xx00 Quad 2-input NAND gate

74xx02 Quad 2-input NOR gate

74xx86 Quad 2-input XOR gate

Note: “xx” refers to the logic family

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Standard Logic Gates Data sheets provide essential information:

Logic Function Truth Table Pin-out Electrical Characteristics Timing Characteristics Package Description(s)

This information is necessary when building logic circuits from discrete components.

Each logic family has a unique set of characteristics.

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Standard Logic Gates: 74xx08

pin-out

Truth table

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Standard Logic Gates: 74xx32

pin-out

Truth table

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Standard Logic Gates: 74xx04

pin-out

Truth table

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Building a Logic Circuit

CircuitDiagram

B

C

A

Finputs output

F = B'.C + A.BBoolean

Expression

74xx08

74xx08

74xx3274xx04

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Building a Logic CircuitV DD

7404

7408 7432

ABC F

components

wires

inputs

output

WiringDiagram

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Draw the circuit diagram and wiring diagram for the following Boolean expression:

F = A'.B + A.B'

Example

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Example

(circuit diagram)

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Example

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Questions?