logic gates-5,6

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Digital design

CHAPTER 2

Logic Gates

Sec 2-7

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Binary logic

Binary variables logic operators.+

1. AND: x . y =xy ; equal 1 ifx=1 &

y=1.

2. OR: x + y ; equal 1 ifx=1ory=1.

3. NOT: x= x .

X , y , z

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The difference between binary arithmetic and binary logic.

binary arithmetic binary logic

Addition :1 + 1 = 10

Multiplication : 1 . 1 = 1

OR: 1 + 1 = 1

NOT: 1 = 1 = 0

NOT: 0 = 0 = 1

AND : 1 . 1 = 1

AND : 1 . 0 = 0

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Truth table of logic operations

111

001

010

000

X.YYX

111

101

110

000

X+YYX

01

10

XX

AND

OR NOT

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Logic Gates Inverter

AND Gate OR Gate

Exclusive-OR Gate NAND Gate

NOR Gate

Exclusive-NOR Gate

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The Inverter

Truth table

0 = LOW1 = HIGH Pulsed waveforms

The output of an inverter is always theThe output of an inverter is always the

complement (opposite) of the input.complement (opposite) of the input.

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The AND Gate

Truth table

0 = LOW1 = HIGH

Pulsed waveforms

The output of an AND gate is HIGH onlyThe output of an AND gate is HIGH only

when all inputs are HIGH.when all inputs are HIGH.

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The AND Gate

33--Input AND GateInput AND Gate

44--Input AND GateInput AND Gate

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The OR Gate

Truth table

0 = LOW1 = HIGH

The output of an OR gate is HIGHThe output of an OR gate is HIGH

whenever one or more inputs are HIGHwhenever one or more inputs are HIGH

Pulsed waveforms

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The OR Gate

33--Input OR GateInput OR Gate

44--Input OR GateInput OR Gate

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The NAND Gate

Truth table

0 = LOW1 = HIGH

The output of a NAND gate is HIGHThe output of a NAND gate is HIGH

whenever one or more inputs are LOW.whenever one or more inputs are LOW.

Pulsed waveforms

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The NAND Gate

33--Input NAND GateInput NAND Gate 44--Input NAND GateInput NAND Gate

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The NOR Gate

Truth table0 = LOW1 = HIGH

The output of a NOR gate is LOWThe output of a NOR gate is LOW

whenever one or more inputs are HIGH.whenever one or more inputs are HIGH.

Pulsed waveforms

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The NOR Gate

33--Input NOR GateInput NOR Gate 44--Input NOR GateInput NOR Gate

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Exclusive-OR Gate

Truth table

0 = LOW1 = HIGH

The output of an XOR gate is HIGHThe output of an XOR gate is HIGH

whenever the two inputs are different.whenever the two inputs are different.

Pulsed waveforms

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Exclusive-NOR Gate

Truth table

0 = LOW1 = HIGH

The output of an XNOR gate is HIGHThe output of an XNOR gate is HIGHwhenever the two inputs are identical.whenever the two inputs are identical.

Pulsed waveforms

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Positive & Negative Logic

In logic gates, usually:

H (high voltage, 5V) = 1

L (low voltage, 0V) = 0

H (high voltage) = 0

L (low voltage) = 1

positive logic

convention

the reverseconvention,

negative logic

MANO sec 2-7

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Positive logic:

Negative logic:

Enable

Active High:

0: Disabled1: Enabled

Enable

Active Low:

0: Enabled

1: Disabled

Positive & Negative Logic

complemented

form.

Un complemented form.

MANO sec 2-7