lecture no. 7
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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
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