G.H. Patel College of Engineering and Technology Subject: Digital Electronics Name Enrollment no. Champaneria Dhvanil J. 150113109004 Chauhan Nisarg D. 150113109005 Jadav Prashant 150113109009 Limbani Milan P. 150113109011
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G.H. Patel College of Engineering and Technology
Subject: Digital Electronics
Name Enrollment no.Champaneria Dhvanil J. 150113109004
Chauhan Nisarg D. 150113109005Jadav Prashant 150113109009
Limbani Milan P. 150113109011
Logic Gates &
Universal Gate
Logic Gate:
Actually the term logic is applied to digital circuits used to implement logic functions. Several kinds of digital logic circuits are the basic elements that form the building blocks for such complex digital system as the computer.
The lines connected to each symbols are the inputs and outputs. The inputs are on the left of each symbol and the output is on the right.
A circuit that performs a specific logic operation (AND, OR) is called a logic gate.
AND Gate:
An AND gate can have two or more inputs and performs what is know as multiplication. The output of AND gate is high when all inputs are high otherwise all outputs are low.
Inputs OutputA B X0 0 00 1 01 0 01 1 1
Logical SymbolTruth Table
• It’s logical expression is, X=A.B
OR Gate:
OR gate can have two or more inputs and performs what is known as logical addition. The output of OR gate is Low when all inputs are low, otherwise all outputs are high
Logical SymbolInputs Output
A B X0 0 00 1 11 0 11 1 1
Truth Table
• It’s logical expression is, X=A+B
Not Gate:
The inverter (NOT circuit) performs the operation called inversion or complementation. The NOT operation changes one logic level to the opposite logical level. When the input is Low, the output
is high. When the input is high, the output is low.
Input Output0 11 0
Logical SymbolTruth Table
• It’s logical expression is, A=A’
NAND Gate:
The NAND gate is the one of the popular logic element because it can be used as a universal gate; that is NAND gate can be used in combination to perform the AND, OR, and inverter operations.
NAND Gate is constructed by attaching NOT Gate at the output of AND Gate, hence NAND Gate is called NOT- AND Gate.
The output of NAND gate is low when all inputs are high, otherwise all outputs are high.
Logical Symbol
It’s logical expression is, X= (AB)’
Inputs OutputA B X0 0 10 1 11 0 11 1 0
Truth Table and Expression of NAND Gate:
NOR Gate:
The NOR gate, like the NAND gate, NOR gate is also useful logical element because it can also be used as a universal gate.
NOR gate can be used in combination to perform the AND, OR and Inverter operations. NOR Gate is the combination of NOT gate at the output of OR gate, hence NOR gate is type of NOT-OR
gate. The Output of NOR gate is high when all inputs are low otherwise the output is low.
Logical Symbol
Inputs OutputA B X0 0 10 1 01 0 01 1 0
It’s expression is, X=(A+B)’
Truth Table and Expression of NOR Gate:
Exclusive- OR Gate:
The exclusive-OR gate has a graphical symbol similar to that of the OR gate, except for the additional curved line on the input side.
If both inputs are Low or both are High then it produces the output Low or 0. otherwise it produce the High.
Logical Symbol
Inputs OutputA B X0 0 00 1 11 0 11 1 0
It’s logical expression is X=AB’+A’B
Truth Table and Expression of Ex-OR Gate:
Exclusive-Nor gate:
The exclusive-NOR gate is the complement of the exclusive-OR gate, as indicated by small circle on the output side of the graphic symbol.
If both inputs are Low or both are High then it produces the output High or 1. otherwise it produce the Low output.
Logical symbol
Inputs OutputA B X0 0 10 1 01 0 01 1 1
It’s logical expression is
Truth Table and Expression of Ex-NOR Gate:
NAND gate as Universal gate
NAND Gate as an AND Gate:
X
Y YX YXZ
YX
NAND Gate Inverter
Logical symbol
Inputs OutputX Y Z0 0 00 1 01 0 01 1 1
Truth Table
NAND Gate as an OR Gate:
X
YYXY X Y XZ
X
NAND GateInverters
Y
Logical symbol
Inputs OutputX Y Z0 0 00 1 11 0 11 1 1
Truth Table
NAND Gate as an NOT Gate:
X XZ
Logical symbol
Input OutputX Z0 11 0
Truth Table
NAND Gate:
X
Y Y X YXZ
Logical symbol
Truth Table
Inputs OutputA B Z0 0 10 1 11 0 11 1 0
NAND Gate as an NOR Gate:Logical symbol
Truth Table
Inputs OutputA B Z0 0 10 1 01 0 01 1 0
NAND Gate as an Ex-OR Gate:Logical symbol
Truth Table
Inputs OutputX Y Z0 0 00 1 11 0 11 1 0
NAND Gate as an Ex-NOR Gate:
Logical symbol
Truth Table
Inputs OutputX Y Z0 0 10 1 01 0 01 1 1
NOR gate as Universal gate
NOR Gate as an AND Gate:
X
YY XY X Y XZ
X
NOR Gate“Inverters”
Y
Logical symbol
Truth TableInputs Output
X Y Z0 0 00 1 01 0 01 1 1
NOR Gate as an OR Gate:
X
Y YX Y XZ
Y X
NOR Gate “Inverter”
Logical symbol
Truth TableInputs Output
X Y Z0 0 00 1 11 0 11 1 1
NOR Gate as an NOT Gate:
X XZ
XXX (Before Bubble)
Logical symbol
Truth Table
Inputs OutputX Z0 11 0
NOR Gate as an NAND Gate:
Logical symbol
Truth Table
Inputs OutputX Y Z0 0 10 1 11 0 11 1 0
NOR Gate:
X
YY X Y XZ
Logical symbol
Truth Table
Inputs OutputX Y Z0 0 10 1 01 0 01 1 0
NOR Gate as an Ex-OR Gate:Logical symbol
Truth Table
Inputs OutputX Y Z0 0 00 1 11 0 11 1 0
NOR Gate as an Ex-NOR Gate:Logical symbol
Truth Table
Inputs OutputX Y Z0 0 10 1 01 0 01 1 1
Thank You…..
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