Digital Electronics

Unit 5
Syllabus
• Analog and digital signal,
• Binary number system,
• logic gates, three basic logic gates - NOT, AND, OR, combination of basic logic
gates,
• NAND and NOR as universal gates,
• EXOR Gates,
• Boolean algebra,
• Boolean theorems,
• De Morgan’s Theorems,
• Developing logic circuit from Boolean expression
Analog and digital signal
• Analog signals are used to
communicate information in a
continuous function of time
while a digital signal transmits
data in a discrete function of
time.
• Analog signals represent data
and information using a
continuous range of values
while digital signals use discrete
values 0 and 1.
Analog and digital signal
Binary number system
• Binary Number System is a number system that is used to represent
various numbers using only two symbols “0” and “1”.
• The word binary is derived from the word “bi” which means two.
Hence, this number system is called Binary Number System.
• Thus, the binary number system is a system that has only two symbols.

• There are generally various types of number systems and among them the four major ones are,
• Binary Number System (Number system with Base 2)
• Octal Number System (Number system with Base 8)
• Decimal Number System (Number system with Base 10)
• Hexadecimal Number System (Number system with Base 16)
Binary number system cont..
• This number system is very useful for explaining tasks to the
computer. In the Binary Number System, we have two states “0” and
“1” and these two states are represented by two states of a transistor.
• If the current passes through the transistor then the computer reads
“1” and if the current is absent from the transistor then it read “0”.
• Thus, alternating the current the computer reads the binary number
system. Each digit in the binary number system is called a “bit”.
Binary Number System
• Binary Number System is the number system in which we use two
digits “0” and “1” to perform all the necessary operations.
• In the Binary Number System, we have a base of 2.
• The base of the Binary Number System is also called the radix of
the number system.
• In a binary number system, we represent the number as,
• (11001)2
• In the above example, a binary number is given in which the base is 2.
In a binary number system, each digit is called the “bit”. In the above
example, there are 5 digits.
BINARY and DECIMAL number representation
 • Let's express a decimal number 1341 in binary notation.
• Note that the desired base is 2, so we repeatedly divide the given
decimal number by 2.

Conversion

Decimal to
Binary
Convert Decimal(fraction to Binary)
Binary to Decimal Conversion
Logic Gates:

• Logic gates are the basic building

blocks of the digital circuits.

• These logic gate circuits are made up

of diodes, transistors and resistors.

• Most of the electronic devices which

we use everyday like our smart
phones, tablet, laptops and memory
devices use logic gates in their
electronic circuits.

• Logic gates have two or more inputs

and one output.

• The inputs and outputs are either ‘0’

or ‘1’. The logic gates take decisions
the output.
 Basic Gates
• AND:
• AND Logic Gate produces the output ‘1’ only
when all the inputs are ‘1’. AND operation is
denoted by ‘*’. This Logic Gate operation is
similar to ordinary multiplication.
• Two input AND gate and its truth table:
• Y= A*B
7400-AND Gate(Quad)/Pin Configuration
Basic Gates - Cont.
Three input OR gate and its truth table:
• OR:
• OR operation is similar to ordinary addition but it is not exactly Y=A+B+C
equal to addition. It is represented by ‘+’. The OR logic gates
produces the output ‘1’ when any one of the input is ‘1’. It
produces the output ‘0’ when all the input is ‘0’.

• Two input OR gate and its truth

table:
• Y=A+B
Basic Gates - Cont.
• NOT:
• NOT gate has only one input and
one output. It is also called as
inverter or complementation. It is
denoted by (').
• Y=A'
Basic Gates - Cont.
• NAND: Three input NAND gate and its truth table:
• NAND gate operation is inversion operation of
AND gate. So the output of the AND gate is Y=(A*B*C)‘
complimented. It produces the output ‘0’ when
all the inputs are ‘1’. It produces ‘0’ for all other
combinations of input.

• Two input NAND gate and its truth table:

• Y=(A*B)'
Basic Gates - Cont.
• NOR: Three input NOR gate and its
truth table:
• NOR gate operation is inversion operation of OR
gate. So the output of the OR gate is
complimented. It produces the output ‘1’ when
all the inputs are ‘0’. It produces ‘0’ for all other
combinations of input.

• Y=(A+B)‘
 Basic Gates - Cont.
• Exclusive–OR (XOR): Three input Ex-OR gate and its
• XOR operation is denoted by encircled plus sign . The truth table:
output is ‘1’ when either of the input is high. When
both the inputs are same, that is when both are ‘1’ or
‘0’, it produces ‘0’ output.

• Two input Ex-OR gate and its

truth table:
Basic Gates - Cont.
• Exclusive–NOR: Three input Ex-NOR gate and its truth
• Ex-NOR is the compliment gate of XOR. It table:
produces the output ‘1’ when both the
inputs are same, that is when both are ‘1’ or
‘0’. It produces the output ‘0’ when either of
the input is ‘1’.
• Two input Ex-NOR gate and its truth table:
Universal Logic Gates-

• Universal logic gates are the logic gates that are capable of
implementing any Boolean function without requiring any
other type of gate.

• They are called as “Universal Gates” because-

• They can realize all the binary operations.
• All the basic logic gates can be derived from them.
• They have the following properties-
• Universal gates are not associative in nature.
• Universal gates are commutative in nature.
Universal Logic Gates-
Universal Logic Gates-
Universal Logic Gates-
Universal Logic Gates-
Universal Logic Gates-
Universal Logic Gates-
Universal Logic Gates-
Universal Logic Gates-
Universal Logic Gates-
Universal Logic Gates-
Universal Logic Gates-
Universal Logic Gates-
Boolean algebra
• Boolean algebra is a branch of mathematics that deals with
operations on logical values with binary variables.

• The Boolean variables are represented as binary numbers to

represent truths: 1 = true and 0 = false.

• Elementary algebra deals with numerical operations whereas Boolean

algebra deals with logical operations.
Boolean Algebra
• Laws of Boolean Algebra
• There are six types of Boolean algebra laws. They are:
• Commutative law
• Associative law
• Distributive law
• AND law
• OR law
• Inversion law
• Those six laws are explained in detail here.
• Commutative Law
• Any binary operation which satisfies the following expression is referred to as a commutative operation.
Commutative law states that changing the sequence of the variables does not have any effect on the
output of a logic circuit.
• A. B = B. A
• A+B=B+A
Boolean Algebra cont..
Boolean Algebra cont..
Boolean Theorems
Boolean Theorems
Boolean Theorems
De Morgan’s First Theorem
De Morgan’s First Theorem
De Morgan’s Second Theorem
De Morgan’s Second Theorem
Developing logic circuit from Boolean expression
Developing logic circuit from Boolean expression

• Other examples can be added…