Introduction
A Logic Gate is an electronic circuit capable of making logical decisions.
It has one output and one or more inputs.
Basic building blocks of digital systems.
0 and 1.
0 means 0 to 0.8 V.
1 means 3 to 5 V.
0.8 V to 3 V is undefined.
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The OR Gate Y = A + B
“The output is high when
one or more inputs are high.”
Meaning of + sign
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Implementation of OR gate
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A Practical Application of OR Gate
Alarm is activated whenever temperature or pressure goes above certain level.
Three-input OR Gate
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Example : Find the OR gate output.
The AND Gate The output is high
when all the inputs are high.
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“Y equals A AND B.”
Implementation of AND gate.
Three-input AND Gate
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Example : Determine the variation with time of the output Y.
Example : Determine the variation with time of the output Y.
B input works as a control.
B = 0 inhibit condition; B = 1 enable condition
The NOT Gate
Y = Ᾱ
Y equals NOT A.
Y equals inverse of A.
Y equals complement of A.
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Summary
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The NOR Gate
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Truth Table of NOR Gate
The output is HIGH only
when all the inputs are LOW.
The NAND Gate
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Truth Table of NAND Gate
The output goes LOW
when all the inputs are HIGH.
Example : Determine the output waveform.
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Example : Determine the output waveform.
Example : Implement the function, using only NOR and NAND gates:
Solution :
Boolean Theorems
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Duality
There are useful identities of Boolean expressions that can help us to transform an expression A into an
equivalent expression B
We can derive additional identities with the help of the dual of a Boolean expression.
The dual of a Boolean expression is obtained by
interchanging Boolean sums and Boolean products and interchanging 0s and 1s.
Duality
Examples:
The dual of x(y + z)
is x + yz.
The dual of -x1 + (-y + z) is
(-x + 0)((-y)z).
The dual of a Boolean function F
represented by a Boolean expression is the function represented by the dual of this
expression.
DeMorgan’s Theorems
1. The complement of a sum equals the product of the complements.
2. The complement of a product equals the sum of the complements.
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A B A B A B A B
Theorems are dual of each other.
Simply exchange OR (+) and AND (∙) sings.
applicable for any number of variables.
D C
B A
D C
B A
D C
B A
D C
B A
Examples
Simplify the following Boolean Expressions :
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( ) a z A BC ( ) b z ( AB C )
( ) c z ( A C ) ( B D )
Solutions
( ) a z A BC A BC
C A B
A C
B A
BC
A
( )
( ) b z ( AB C ) ( AB C ) ( A B C ) C
B A ).
(
C B C
A
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( )c z (A C ) ( B D) (A C ) ( B D)
( ) ( )
z A C B D AC BD
Implications of
De Morgan’s Theorems
Alternative symbol of NOR function.
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Alternative symbol of NAND function.
UNIVERSAL GATE
Basic gates are OR, AND and NOT.
Any function can be implemented using the above.
However, it is possible to implement any logic function using NAND gates only.
So, NAND gate is called universal gate.
Similarly, NOR gate is also universal gate.
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NAND Gate
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NOR Gate
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7400 IC – a quad
XOR Gate
(Exclusive-OR Gate)
Output is HIGH whenever two inputs are at
opposite levels.
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Logic circuit of XOR Gate
XNOR Gate
(Exclusive-NOR Gate)
Output is HIGH
whenever two inputs
are at same level.
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