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Lecture No. 7

Computer Logic Design

Logic Gates

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NAND Gate

• Contraction of NOT-AND

• Standard logic symbol

• Output is LOW only when all inputs are HIGH

• Bubble indicates ACTIVE LOW output

• Output level is opposite to that of the AND gate

BAF

NCBAF ....

BAF

NCBAF ....

E

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NAND Gate

• The truth table for a two input NAND gate

InputMiddle Output Output

A B E F

0 0 0 1

0 1 0 1

1 0 0 1

1 1 1 0

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NAND Gate

• Timing diagram of NAND gate

t0 t4 t5 t6t1 t2 t3

A

B

F

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NAND Gate

• NAND gate application example– Device Failure Alarm System

– When all the fans are working, the input to the NAND gate is 111 and the output is 0

– If any one of the fan stops working, the output of the NAND gate becomes 1, which activates the alarm

ALARM

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NAND Gate as Negative-OR

• The truth table for a two input NAND gate looks awfully similar to an OR gate with the inputs inverted.

Input NAND Output

A B F

0 0 1

0 1 1

1 0 1

1 1 0

Input OR Output

A B F

1 1 1

1 0 1

0 1 1

0 0 0

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NAND Gate as Negative-OR

Bubble signifies ACTIVE LOW INPUT

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NAND Gate as a Universal Gate

• NAND gate can be used to perform all the fundamental gate operations (NOT, AND, OR)– Universal NAND gate

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NAND as NOT Gate

Input Output

A B F

0 0 1

0 1 1

1 0 1

1 1 0

Join all the input pins of the NAND gate together

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NAND as AND Gate

• Using NAND gate to perform the AND gate operation

• Remember NAND is NOT-AND. What if we inverse this one more level? NOT-(NOT-AND) = AND

• Accomplished by applying a NOT operation (implemented through NAND gate) to the output of the NAND gate

1 2

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NAND as OR Gate

• Using NAND gate to perform the OR gate operation

– Can we form NOR gate as well?

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NOR Gate

• Contraction of NOT-OR• The standard logic symbol

• Produces a LOW output when one or more of its input is HIGH

• Bubble indicates ACTIVE LOW output• The output logic is opposite to that of the OR gate

BAF

NCBAF ....

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NOR Gate

• Truth table for a two input NOR gate

Input Output

A B F

0 0 1

0 1 0

1 0 0

1 1 0

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NOR Gate

• Timing diagram of a NOR gate

t0 t4 t5 t6t1 t2 t3

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NOR Gate as Negative-AND

• The truth table for a two input NOR gate looks awfully similar to an AND gate with the inputs inverted.

Input NOR Output

A B F

0 0 1

0 1 0

1 0 0

1 1 0

Input AND Output

A B F

1 1 1

1 0 0

0 1 0

0 0 0

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NOR Gate as Negative-AND

Bubble signifies ACTIVE LOW INPUT

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NOR Gate as a Universal Gate

• NOR gate can be used to perform all the fundamental gate operations (NOT, AND, OR)– Universal NOR gate

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NOR as NOT Gate

Input Output

A B F

0 0 1

0 1 0

1 0 0

1 1 0

Join all the input pins of the NOR gate together

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NOR as OR Gate

• Using NOR gate to perform the OR gate operation• Remember NOR is NOT-OR. What if we inverse

this one more level? NOT-(NOT-OR) = OR

• Accomplished by applying a NOT operation (implemented through NOR gate) to the output of the NOR gate

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NOR as AND Gate

• Using NOR gate to perform the AND gate operation

– Can we form NAND gate as well?

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XOR Gate• Exclusive OR (XOR for short)

– Standard logic symbol

– This gate has only two inputs

– Logical expression

– The output is HIGH only when the two the inputs are at opposite logic level

BAF

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XOR Gate

• The truth table for XOR Gate

Input Output

A B F

0 0 0

0 1 1

1 0 1

1 1 0

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XOR Gate

• Timing diagram of XOR gate

t0 t4 t5 t6t1 t2 t3

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XNOR Gate

• Exclusive-NOR (XNOR for short)– Standard logic symbol

This gate has only two inputs

– Logical expression

– The output is LOW only when the two inputs are at opposite logic level

BAF

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XNOR Gate

• Truth table for XNOR gate

Input Output

A B F

0 0 1

0 1 0

1 0 0

1 1 1

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XNOR Gate

• Timing diagram of XNOR gate

t0 t4 t5 t6t1 t2 t3

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Summary of logic gates• Fundamental logic gates

– AND– OR– NOT

• Universal gates– NAND– NOR

• Other gates– XOR– XNOR

• Standard logic symbol• Logical/Boolean expression• Truth table• Application example