Digital Electronics

1. Sanjivani Rural Education Society’s
Sanjivani College of Engineering, Kopargaon-423 603
(An Autonomous Institute, Affiliated to Savitribai Phule Pune University, Pune)
NACC ‘A’ Grade Accredited, ISO 9001:2015 Certified
Department of Computer Engineering
(NBA Accredited)
Prof. S.A.Shivarkar
Assistant Professor
Contact No.8275032712
Subject- Digital Electronics and Data
Communications(CO204)
Unit 1- Logic Minimization

2. • To understand Boolean Variable
• To understand Truth table.
• Logic Gate
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3. • The variable in Boolean algebra are allowed to take either value 1 or 0.
• Voltage level on wire or input / output terminal of circuit.
• Value 0 may be assigned to a variable for representing any voltage between range
0V to 0.8V
• Similarly value 1..
• So Boolean 1 and 0 do not represent number but …
• In Boolean algebra there are only 3 basic operation which can be performed on
Boolean variables (AND, OR, NOT).
• These operation are logic operations!!
• How to perform these operation in Digital circuit?
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4. • Describes how digital circuits output depends on input!!
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5. What is Gate?
These are building blocks from which all other digital systems are
constructed.
There are three elementary logic gates.
Each gate has its own logic symbol which allows complex functions to
be represented by a logic diagram
The function of each gate can be represented by a truth table or using
Boolean expression
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6.  NOT
 AND
 OR
 NAND
 NOR
 EX-OR
 EX-NOR
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7.  NOT gate takes only 1 input value and produces 1 output value
 If the input value for a NOT gate is 0, the output value is 1, and if the
input value is 1, the output is 0
 NOT gate is also called as an Inverter.
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8.  Boolean Expression
Y=A’
 Logic Gate Symbol
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A (Input) Y(Output)
0 1
1 0
 Truth table
 Timing Diagram

9.  It performs AND operation on circuits input.
 AND gate take two or more input values and produces one output
value
 If all input values are 1 then output =1 otherwise output=0
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10.  Logic Gate Symbol
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Input Output
A B Y=A.B
0 0 0
0 1 0
1 0 0
1 1 1
 Boolean Expression
 Y=A.B
 Truth table
 Timing Diagram

11.  OR gate take two or more input values and produces one output
value
 Output is equal to OR combination of inputs.
 If all input values=0 then output=0 otherwise output=1
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12.  Boolean Expression
 Y=A+B
 Truth table
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Input Output
A B Y=A+B
0 0 0
0 1 1
1 0 1
1 1 1
 Logic Diagram Symbol
 Timing Diagram

13.  NOR gate take two or more input values and produces one output
value
 It is OR gate followed by inverter
 Also called as Universal gate
 Y=AB+BC’
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14.  Boolean Expression
 Y=(A+B)’
 Truth Table
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Input Output
A B Y=(A+B)’
0 0 1
0 1 0
1 0 0
1 1 0
• Logic Symbol
• Timing Diagram

15.  NAND gate take two or more input values and produces one output
value
 AND gate followed by inverter
 Also called as Universal gate
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16.  Boolean Expression
 Y=(A.B)’
 Truth table
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Input Output
A B Y=(A.B)’
0 0 1
0 1 1
1 0 1
1 1 0
 Logic Symbol
 Timing Diagram

17.  Also called as Exclusive-OR
 XOR gate take two or more input values and produces one output
value
 An XOR gate produces 1 if number of true inputs are odd else
output 0.
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18.  Boolean Expression
 Y= A ⊕ B
 Logic Symbol
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Input Output
A B Y= A ⊕ B
0 0 0
0 1 1
1 0 1
1 1 0
 Truth table

19.  Also called as Exclusive-NOR
 The exclusive-nor gate or EX-NOR is logically equivalent to an Ex-OR
gate followed by an inverter
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20.  Boolean Expression
 Y= (A ⊕ B)’
 Logic Symbol
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Input Output
A B Y=( A ⊕ B)’
0 0 1
0 1 0
1 0 0
1 1 1
 Truth table