The document discusses digital circuits including combinational and sequential circuits. It describes various combinational logic circuits such as half adders, full adders, comparators, multiplexers, encoders, decoders. It also discusses sequential circuits and how they employ memory elements. Arithmetic circuits, binary adders, subtractors, and BCD to 7-segment decoders are explained in detail through diagrams and examples.

1. PREPARED
BY
NABARUN CHAKRABORTY
Assistant Professor
BARAK VALLEY ENGINEERING COLLEGE
KARIMGANJ, ASSAM

2.  Digital Circuits- Combinational & Sequential
 Classification of Combinational Circuits
 Arithmetic Circuits- Half Adder/Full Adder, Half
Subtractor/ Full Subtractor.
 Binary Adder (Asynchronous Ripple- Carry Adder)
 Binary Adder Subtractor
 Digital Comparator
 Parity Checker/Generator
 Multiplexer & Demultiplexer
 Encoder & Decoder.
 BCD to 7-Segment Decoders.

3.  Combinational circuit consists of logic gates whose outputs
at any time are determined directly from the present
combination of inputs without regard to previous inputs.
 Sequential Circuit employ memory elements in addition to
logic gates. Their outputs are a function of the inputs and
the state of the memory elements.

5.  A Combinational circuit consists of input variables, logic
gates and output variables. The gates accept signals from
the Inputs and generate signals to the outputs.

6.  Minimum no. of gates.
 Minimum no. of inputs to the gates.
 Minimum propagation time of the signal through the
circuit.
 Minimum no. of interconnections and
 Limitations of the driving capabilities of each gate.

7.  Half adder is a combinational logic circuit with two inputs
and two outputs.
 The half adder circuit is designed to add two single bit
binary number A and B.
 It is a basic building block for addition of two single bit
numbers.

11.  Full adder is a combinational logic circuit with three
inputs and two outputs.
 The three input are two bits to be added and an incoming
carry while output bits are sum bits and a carry.

16. ▪ Half subtractor is a combinational logic circuit with
two inputs and two outputs (Difference & Borrow)
▪ It produces the difference between the two binary bits
at the input and also produces an output (Borrow) to
indicate if a 1 has been borrowed..

20.  Full subtractor is a combinational logic circuit with three
inputs and two outputs.
 The input are two A, B, Bin while output is Difference &
Borrow.

25.  A binary adder is a digital circuit that produces the
arithmetic sum of two binary numbers.
 A binary adder can be constructed with full adders
connected in cascade with the output carry form each full
adder connected to the input carry of the next full adder in
the chain.
 The four-bit adder is a typical example of a standard
component .It can be used in many application involving
arithmetic operations.

28. The addition and subtraction operations can be combined
into one circuit with one common binary adder by
including an exclusive-OR gate with each full-adder.

29.  A comparator is a logic circuit used to compare the
magnitude of two binary numbers.
 Depending on the design, it may either simply provide an
output that is active (goes HIGH for example) when two
numbers are equal, or additionally provide outputs that
signify which of the numbers is greater when equality
does not hold.

31.  X-OR gates are very useful in systems requiring error detection
& correction codes.
 Binary data when transmitted through air interface can get
corrupted which changes 0’s to 1’s and 1’s to 0’s.
 To detect such errors a “PARITY BIT” is added to data bits and
are transmitted.
 At the receiver end the number of 1’s is counted and error if
any is detected.
 The Parity check can detect only single bit errors.
 In order to check or generate proper parity bits basic principle
is “ The modulo sum of even number of 1’s is always 0 and
modulo sum of odd number of 1’s is always 1”.

34.  Multiplexer is a special type of combinational circuit
which has a number of inputs but only one output.
 Multiplexer is a circuit which transmits large number of
information signals over a single line.
 Multiplexer is also known as “Data Selector” or MUX.
 In most of the electronic systems, the digital data is
available on more than one lines. It is necessary to route
this data over a single line. Under such circumstances we
require a circuit which select one of the many inputs at a
time and the circuit is MULTIPLXER.

36. ▪ There is also an Enable Input which when “0” the
MUX is in OFF state and when “1” is in ON state.

41.  In a 8:1 MUX, there are 3 select lines to choose from a
total combination of 8 input lines and by means of 3 select
lines one combination can be chosen at a time.
 We need three (3) select lines because 2^(3)=8 and 8
combinations of input can easily be handled by using 3
select lines.
 Moreover we also have a Enable Input, which should
mandatorily be at Logic 1 i.e HIGH (or in electrical terms
it should have 5V or 15V)

42. SELECT LINES

44. SELECT LINES

45.  It reduces the number of wires.
 So it reduces the circuit complexity and cost.
 We can implement many combinational circuits using
MULTIPLEXER.
 It simplifies the logic design.
 It does not need the k-map and simplification

46.  It is used as a data selector to select one out of many data
inputs.
 It is used for simplification of logic design.
 It is used in data acquisition system.
 In designing the combinational circuits.
 In Digital to Analog converters.
 To minimize the number of connections.

51.  A de-multiplexer performs the reverse operation of a
multiplexer i.e. it receives one input and distributes it over
several outputs.
 At a time only one output line is selected by the select
lines and the input is transmitted to the selected output
line.
 It has only one input line, n number of output lines and m
number of select lines.

62.  An encoder is a device whose input are decimal digits
and/or alphabetic character and whose outputs are coded
representation of those inputs.
 In other words an encoder is a device which converts
familiar numbers or symbols into coded format.
 Encoder performs encoding i.e encoding is the process of
converting familiar numbers or symbols into a coded
format.
 An encoder has a number of input lines, only one of which
is activated at a given time, and produces an N-bit output
code depending on which input is activated.

63. ▪ This is the block diagram
of an encoder.
▪It has 2^(n) input lines
and n output line.
▪It is more or less similar
to MUX.

64.  Let 4 to 2 Encoder has four inputs Y3, Y2, Y1 & Y0 and
two outputs A1 & A0. The block diagram of 4 to 2
Encoder is shown in the following figure.

66. ▪The above circuit contain only two OR gates

67.  An Octal to Binary Encoder (8:3 Line Encoder) accepts 8
input line and produces 3 bit output code corresponding to
activated input.
Block Diagram of 8:3 Line Encoder

70.  In a decimal to BCD encoder we have 10 inputs-one for
each decimal digit and 4 outputs corresponding to BCD
Code
 This a basic 10:4 line encoder.

72.  From the table we get
 Y3=D8+D9
 Y2= D4+D5+ D6+D7
 Y1= D2+D3+ D6+D7
 Y0= D1+D3+ D5+D7+D9

74.  A decoder is a logic circuit that converts an N-bit binary
input code into M-output lines such that only one output
line is activated for each one of possible combinations of
inputs.
 In other words a decoder identifies or recognizes or
detects a particular code.
 Since N inputs can be a 0 or a 1, there are 2^(N) possible
input combinations or codes. For each of these input
combinations only one of M outputs will be active
(HIGH) all other outputs will remain inactive (LOW).

77.  It has three inputs and eight outputs.
 It uses all AND gates and therefore outputs are all active
HIGH.
 For active LOW input NAND gates are used.
 It is also called Binary to Octal Decoder because it takes
3-bit binary input code and activates one of the eight
(octal) outputs corresponding to that code.
 It is also referred to as 1-of-8 decoder because only one of
eight outputs is activated at one time.

78. ▪ There are three input A,B & C and corresponding to
three inputs we have 8 outputs.
▪Combination of A,B & C gives one output at a time.

80.  This type of decoder accepts the BCD Code and provides
outputs to energize seven segment display devices in order
to produce a decimal read out.
 Sometimes HEX Characters A-F may also be produced.
 Each segment is made up of material that emits light when
current flows through it.
 Common examples are LED’s, Incandescent Filaments
and LCD’s.
 The seven segment display has seven light emitting
segments.

83.  In common anode LED, a low voltage applied to an LED
cathode allows current to flow through the diode which
causes it to emit light.
 In common cathode type, a high voltage is applied to an
LED anode causes current to flow and produce resulting
light emission.