digita circuit design.pptx

CONTENTS :
• Logic Gates.
• Boolean Algebra
• Map Simplification.
• Combinational Circuit.
• Flip Flop.
• Sequential Circuit.

LOGIC GATES
* A logic gate is an electronic circuit which
makes logical decisions, the most common logic
gates are AND, OR, NOT gates.
* The NAND and NOR gates are called as the
Universal gates.
* The exclusive OR gates is another logic gate
which can be constructed using basic gates such as
AND, OR, NOT.
* There are more type of logic gates.

Logic Gates :
* OR Gate.
* AND Gate.
* NOT Gate.
* NAND Gate.
* NOR Gate.
* Exclusive-OR(Ex-OR) Gate.

OR Gate :
* The OR gate performs Logic addition, it
is known as OR function.
* The OR gate has two or more inputs
and only one output.
Y = A+B
The OR function can be expressed as
Y = A+B+C+D+……..

A
Y=A+B
Input Output
Y= A+B
A B
0 0 0
0 1 1
1 0 1
1 1 1
B
a) Logic Symbol
b) OR gate truth table

AND GATES :
* The AND gate performs logical
multiplication, it is known as AND
function.
* The AND gate has two or more input
and a single output.
Y= A . B
* Where the dot(.) denotes the AND
operation.
Y =AB

A
Y=AB
Input Output
Y= AB
A B
0 0 0
0 1 0
1 0 0
1 1 1
B
a) Logic Symbol
b) AND gate truth table

NOT GATE :
* The NOT gate performs the basic
logical function called inversion or
complementation.
* The purpose of the gate is to convert
one logic level into the opposite logic level.
Input
A
Output
Y = A
0 1
1 0
Y= A
A
a) Logic Symbol
b) NOT gate truth table

NAND GATE :
* NAND is a contraction of the NOT-AND
gates.
* It has two or more inputs and only one
output.
Input Output
Y= AB
A B
0 0 1
0 1 1
1 0 1
1 1 0
A
B
a) Logic Symbol
b) NAND gate truth table
Y=AB

NOR GATE :
 NOR is a contraction of NOT-
OR gates.
 It has two or more inputs and
only one output.
A Y=A+B
Input Output
Y= A+B
A B
0 0 1
0 1 0
1 0 0
1 1 0
B
a) Logic Symbol
b) NOR gate truth table

EXCLUSIVE-OR(EX-OR) GATE :
* An Exclusive-OR gate is a gate with
two or more inputs and one output.
* The output of a two-input Ex-OR gate a
HIGH state.
Y=A +
B
a) Logic Symbol
b) Ex-OR gate truth table
Inp ut Output
A B Y= A +B
0 0 0
0 1 1
1 0 1
1 1 0

BOOLEAN ALGEBRA
* Boolean Algebra , elements have one of
two values –True or False.
* The circuits in a computer are also
designed for two-state operations.
* That is input and output of a circuit is
either low(0) or high(1).
* The circuits are called logic circuits.

BOOLEAN ALGEBRA :
 There are three basic operators in Boolean Algebra
which are called logical operators or Boolean
operators.
1. OR - logical addition
2. AND – logical multiplication
3. NOT – Logical negation
 The Boolean operators are used to combine Boolean
variables and Boolean constants to form Boolean
Expressions.

NOT OPERATION
DeMorgan’s law :
1. (A.B)’= A’+ B’
2. (A+B)’= A’. B’

BOOLEAN ALGEBRA
• The sum-of-products form
for our function is:
We note that this function is not in
simplest terms. Our aim is only to
rewrite our function in canonical
sum-of-products form.

MAP SIMPLIFICATION
K – Map Simplification :
K-map method can also be used for
simplifying the logic expression for s and c-
out.
0 1 0 1
1 0 1 0
0 0 1 0
0 1 1 1
AB
C out
C out
AB
00 01 11 10
00 01 11 10
0
1
0
1
a) K-map for Sum
b) K-map for C out

1
3
B
A 0
0
2
B
1
A
1
TWO VARIABLE
K-MAP
Three variable
BC
A
0
1
B
00 01 11 10
0 1 3 2
4 5 7 6
A
C
Four Variable k-map
AB
CD
00 01
00 0 1
01 4 5
11 12 13
10 8 9
A
B
C
11 10
3 2
7 6
15 14
11 10

EXAMPLE FOR K – MAP :
Product of sum simplification
Formula : F’ = AB+CD+BD’
F = (A’+B’)(C’+D’)(B’+D)
1
0
1
1
0
0
1
0
0 0 0 0
1 0
1 1

COMBINATIONAL CIRCUITS
Combinational logic circuits are circuits in
which the output at any time depends upon the
combination of the input signals.
* Multiplexers
* De-Multiplexers
* Encoders
* Decoders

MULTIPLEXERS (DATA SELECTORS)
Multiplexer
1 output
signal
* The term ‘multiplex’ means “many into one”.
Multiplexing is the process of transmitting a large number of
information over a single line.
* A digital multiplexer is a combinational circuit that
selects one digital information from several source and
transmits the selected information on a single output line.
* A multiplexer is also called a data selector.
m select signals
n input
signal

DE-MULTIPLEXERS(DATA DISTRIBUTORS)
* The “demultiplex” means “one into many”.
* Demultiplexing is the process of taking information
from one input and transmitting the same over one of several
output.
* A demultiplexer is a receives
information on a single input
logic circuit the
and transmits the same
Demultiplexer 1 output
signal
information over one for several (2n) output lines.
m select signals
n input
signal

ENCODERS
* An encoder is a digital circuit that performs the
inverse operation of a decoder and the opposite of the
decoding process is called encoding.
* Encoder is a combinational logic circuit that convert
an active input signal into a coded output signal.
Encoders
m outputs
n input

OCTAL-TO-BINARY ENCODER :
IT IS WELL-KNOWN THAT A BINARY-TO-
OCTAL DECODER A 3- BIT INPUT CODE AND
ACTIVATES ONE OF EIGHT OUTPUT LINES
CORRESPONDING TO THAT CODE.
.
Input Output
D0 D1 D2 D3 D4 D5 D6 D7 Y2 Y1 Y0
1 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 1
0 0 1 0 0 0 0 0 0 1 0
0 0 0 1 0 0 0 0 0 1 1
0 0 0 0 1 0 0 0 1 0 0
0 0 0 0 0 1 0 0 1 0 1
0 0 0 0 0 0 1 0 1 1 0
0 0 0 0 0 0 0 1 1 1 1

* An decoder is similar to demultiplexer but
without any data input. It is most digital systems
require the decoding of data.
* Decoding is necessary in applications such as
data demultiplexing, digital display, digital-to-
analog converters and memory addressing.
* Each output line will be activated for only one
of the possible combinations of inputs.
* A decoder is a number of output is greater
than the number of inputs.
DECODERS

3-TO-8 DECODER :
A 3-TO-8 DECODER HAS THREE INPUT
(A,B,C) AND EIGHT OUTPUT(D0 TO D7)
BASED ON 3 INPUT ONE OF THE EIGHT
OUTPUT IS SELECTED.
Input Output
A B C D0 D1 D2 D3 D4 D5 D6 D7
0 0 0 1 0 0 0 0 0 0 0
0 0 1 0 1 0 0 0 0 0 0
0 1 0 0 0 1 0 0 0 0 0
0 1 1 0 0 0 1 0 0 0 0
1 0 0 0 0 0 0 1 0 0 0
1 0 1 0 0 0 0 0 1 0 0
1 1 0 0 0 0 0 0 0 1 0
1 1 1 0 0 0 0 0 0 0 1

FLIP FLOPS
* The simplest kind of sequential circuit is
a memory cell that has only two states it is
called flip flop.
* It is used to store One bit of information
with a 0 or a 1.
* A flip flop is also known as bistable,
multivibrator, latch or toggle.

Type of Flip Flop :
* Flip flop are of different types
depending on the input and clock pulses
cause transition between two states.
* There are four type of flip flop.
* S-R Flip flop (Set/Reset).
* D Flip flop (Delay/Data).
* J-K Flip flop.
* T Flip flop (Toggle).

WORKING OF S – R FLIP FLOP (SET/RESET) :
* If both S and R are 0 during transition, the
output does not change.
* If S= 1 and R= 0, the out put Q is set to 1.
* If S= 0 and R=1, the output is cleared or reset
to 0.
* If both S and R are 1, the output is
unpredictable. This condition makes the RS flip flop
difficult to manage and therefore is forbidden in
practice.

WORKING OF D – FLIP FLOP :
The D input goes directly into the S
input and the complement of the D input
goes to the R input.
* If it is 1, the flip-flop is switched to
the set state (unless it was already set).
* If it is 0, the flip-flop switches to
the clear state.
Applications:
1. Registers as storage devices.
2. Used as a Buffer. 3. In Digital system.

WORKING OF JK – FLIP FLOP :
* When j and k both are 0, the data inputs
have no effect on the outputs.
* When j=0 and k=1, the flip flop is reset
or cleared to 0.
* When j=1 and k=0. the flip flop is set to
1.
* When j and k are 1, if the state of flip
flop was 0,applying a clock with 1and flip
flop state was 1, it changes to 0.

* This on off state is TOGGLING.
* Racing condition: Toggling between 0
to 1 and 1 to 0 alternatively for one clock
cycle.
Application:
1. Counters.
2. Frequency Dividers.
3. Register.

WORKING FOR T – FLIP FLOP :
* The T - flip flop is also known as the
TOGGLE - flip flop. The toggle mode of JK flip
flop is used as T - Flip flop.
* This Flip flop can be obtained from a JK
flip flop when inputs J and K are connected to
provide a single input designated by T.
* The T flip-flop is a single input version of
the JK flip - flop. The T flip flop is obtained from
the JK type if both inputs are tied together.

* The output of the T flip-flop "toggles" with
each clock pulse.
* When t=0, (j=0, k=0) the clock transition
does not change.
* When t=1, (j=1, k=1) the clock transition
complements the state.

SEQUENTIAL CIRCUIT
* Sequential Logic circuits remember
past inputs and past circuit state.
* Outputs from the system are “fed
back” as new inputs
With gate delay and wire delay
* The storage elements are circuits
that are capable of storing binary
information: memory

SEQUENTIAL CIRCUITS :
Circuits that we
have learned
so far
Information Storing
Circuits
Timed “States”
Sequential Circuits Diagram

SYNCHRONOUS SEQUENTIAL CIRCUITS: FLIP
FLOPS AS STATE MEMORY
The flip-flops receive their inputs from the
combinational circuit and also from a clock signal
with pulses that occur at fixed intervals of time, as
shown in the timing diagram.

digita circuit design.pptx

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digita circuit design.pptx