Chapter 2 Logic Gates
Logic Gates
• The basic building block of a digital circuit is a logic gate. • OR, AND and NOT gates are the most basic logic gates. • NOR, NAND, XOR and XNOR gates are constructed using these three basic gates. • Logic gates operate with binary numbers.
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Binary 0
• LOW voltage • +0 volt
Binary 1
• HIGH voltage • +5 volt RA/Sept2012-Jan2013
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Logic Gates
NOT AND
XNOR
Basic Gates
XOR
NOR
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OR
NAND
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NOT Gate (Inverter)
Description
• Inverter is a logic circuit that inverts or complements its output. • If the input is 0, the output will be 1 and vice-versa.
Symbol
•
Logic Expression
• Y=A
Truth table
•
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A
Y
A (Input)
Y (Output)
0
1
1
0
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4
AND Gate
Description
• An AND gate can have two or more inputs and performs a logical multiplication. • It produces HIGH output only when all of the inputs are HIGH. • In other words, the output of an AND gate is 1 if all of the inputs are 1.
Symbol
• •
Logic Expression
• Y = AB
Truth table
•
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A B
Y
A
B
Y
0
0
0
0
1
0
1
0
0
1
1
1 RA/Sept2012-Jan2013
Serial Circuit A
B Y
Lamp Y will light when both of the input switches are closed. 5
OR Gate
Description
• An OR gate can have two or more inputs and performs a logical addition. • It produces HIGH output when one or more inputs are HIGH. • In other words, the output of an OR gate is 1 if any of the inputs are 1.
Symbol
• A • B
Logic Expression
• Y=A
+B
Truth table
•
A
B
Y
0
0
0
0
1
1
1
0
1
1
1
1
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Y
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Parallel circuit A B Y
Lamp Y will light when either or both of 6 the input switches are closed.
NAND Gate
Description
• NAND gate is an AND gate followed by an inverter. • It produces LOW output only when all the inputs are HIGH. • In other words, the output of an AND gate is inverted to form a NAND gate.
Symbol
• •
Logic Expression
• Y = A.B
Truth table
•
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A B
Y
A
B
Y
0
0
1
0
1
1
1
0
1
1
1
0 RA/Sept2012-Jan2013
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NOR Gate
Description
• NOR gate is an OR gate followed by an inverter. • It produces LOW output when one or more of the inputs are HIGH. • The output of an OR gate is inverted to form a NOR gate.
Symbol
• A • B
Logic Expression
• Y=A
Truth table
•
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Y
+B
A
B
Y
0
0
1
0
1
0
1
0
0
1
1
0 RA/Sept2012-Jan2013
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Exclusive-OR (XOR) Gate
Description
• A logic gates that produces a HIGH output only when an odd number of 1s appear at the inputs.
Symbol
• •
Logic Expression
• Y=A
Truth table
•
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A B
Y
+B
A
B
Y
0
0
0
0
1
1
1
0
1
1
1
0
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Exclusive-NOR (XNOR) Gate
Description
• A logic gates that produces a LOW output only when an odd number of 1s appear at the inputs. • In other words, the output of an XNOR gate is the complement of the XOR gate.
Symbol
• A • B
Logic Expression
• Y=A
Truth table
•
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Y
+B
A
B
Y
0
0
1
0
1
0
1
0
0
1
1
1 RA/Sept2012-Jan2013
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Test Yourself
1. Derive the truth table and draw the logic circuit for the following Boolean expressions. Y A B C
a)
b)
Y A B AC
2. Write the Boolean expression for Y. a)
b) A
A Y
B
B Y C
C
D D
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