Centennial College
School of Engineering Technology &
Applied Science (SETAS)
Sustainable Design & Renewable
Energy (SDRE)
ESET211 – Digital and Power Electronic
Week#4 – Combinational Logic Circuits
Week#4 Learning Outcome
1. Combinational Logic
1. Comparators
2. Decoders
3. Encoders
4. Multiplexers
5. Demultiplexers
2. Summary
2
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1.1- Comparators(1)
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A number of standard combinational logic functions
have been developed for digital circuits that represent
many of the useful tasks that can be performed with
digital circuits.
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Often it is important to compare two
binary strings to determine if they are
exactly equal.
This comparison process is performed
by a digital comparator.
The basic comparator evaluates two
binary strings bit by bit and outputs a 1
if they are exactly equal. An XNOR gate
is the easiest way to compare the
equality of bits.
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1.1- Comparators(2)
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Magnitude Comparators
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A=B
A>B
A<B
7485 TTL 4-bit comparator
Source: 74HC85 datasheet –Philips Semiconductor
4
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1.1- Comparators(3)
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5
By using this IC we can build higher-bit comparator, for
example let’s implement 8-bit comparator by using 74HC85:
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1.2- Decoders (1)
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6
The general function of a decoder is to activate one or more
circuit outputs upon detection of a particular digital state.
Single-Gate Decoder is a simplest single gate, sometimes in
combination with one or more inverters, used to detect the
presence of one particular binary value.
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The following figures show two decoders, both of which detect an
input.
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The first decoder generates a logic HIGH when its input is 1111.
The second decoder responds to the same input, but makes the
output LOW instead. The gates in both figures have outputs with
opposite active levels.
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1.2- Decoders (2)
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7
Multiple-Output Decoders circuits often are constructed
with multiple outputs. Such a device is a collection of
decoding gates controlled by the same inputs. A decoder
circuit with n inputs can activate up to m = 2n load circuits.
Such a decoder is usually described as an n line- to-m-line
decoder.
Consider the logic
circuit of a 2-lineto-4-line decoder.
The circuit detects
the presence of a
particular state of
the 2-bit input
D1D0, as shown
by the truth table
Only one output is HIGH
for any Input combination,
provided the enable input
G is LOW.
 The subscript of the active
output is the same as the
value of the 2-bit input.
 If , D1D0=10 output Y2 is
active (since 10 = 2 (decimal)).
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1.2- Decoders(3)
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8
3-Bit Binary-to-Octal Decoder Truth Tables
Complete Octal Decoder (active LOW outputs)
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1.2- Decoders(4)
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Octal Decoder
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Also known as 1-of-8 decoder
Also known as 3-line-to-8-line decoder
74138 pin configuration and logic symbol.
Enables
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1.2- Decoders(5)
A0
A0
A1
A1
A2
A2
\E1
\E1
\Y0
\Y0
\Y3
\Y3
\Y5
\Y5
10
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1.2- Decoders (6)
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7442 BCD-to-DEC Decoder IC
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11
1-of-10 decoder pin configuration and logic
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1.2- Decoders(7)
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74154 Hexadecimal Decoder IC
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1-of-16 Decoder pin configuration and logic symbol
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1.2- Decoders (8)
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13
The seven-segment display is a numerical display device used to show
digital circuit outputs as decimal digits (sometimes hexadecimal digits).
It consists of seven luminous segments (light-emitting diodes LED or liquid
crystals). Since a LED is a diode, it conducts when its anode is positive with
respect to its cathode.
It is conventional to designate the top segment as a, and progress clockwise
around the display, ending with g, as the centre element.
A series resistor limits the current to prevent the diode from burning out and
to regulate its brightness.
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1.2- Decoders(9)
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7447 BCD to 7-sgement display decoder :
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A0, A1, A2, A3
a, b, c, d, e, f, g
BCD Inputs
Active Low Outputs
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1.3- Encoders (1)
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15
Encoding is the opposite process from decoding. It is used
to generate a coded output (like BCD or binary) from a
singular active numeric input line.
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For 2n number of input it provides n output.
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A basic decimal-to-BCD encoder:.
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1.3- Encoders (2)
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74147 Decimal-to-BCD Encoder
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16
Inputs and outputs are Active-LOW
Note bubbles on logic symbols
Priority encoder - highest input has priority
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1.3- Encoders (3)
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74148 Octal-to-Binary Encoder:
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Eight active-low inputs
Three active-low outputs
Priority encoder
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1.3- Encoders (4)
18
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1.3- Encoders (5)
19
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1.4- Multiplexers (1)
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A device capable of funneling
several data lines into single line
for transmission to another point.
It consists of several input lines
and control signals( data selectors )
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Data select control determines which
input is transmitted
Multiplexers can be used to
implement combinational logic
circuits.
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1.4- Multiplexers(2)
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74151 Eight-Line Multiplexer logic symbol
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21
Note 3 data select inputs for 8 inputs (23 = 8)
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1.4- Multiplexers(3)
22
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1.5- DeMultiplexers (1)
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Opposite procedure from multiplexing
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Selectors pick which output path for the
incoming input
Single data input routed to one of several
outputs
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1.5- DeMultiplexers (2)
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74139 Dual 4-line Demultiplexer logic symbol and logic
diagram
74139 connected to
route an input signal to
the 2a output
24
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1.5- DeMultiplexers (3)
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74154 4-line-to16-line hexadecimal decoder
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Used as a 16 line demultiplexer
Connected to
route a signal to
the 5 output
25
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2 – Summary
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Comparators can be used to determine equality or which of two
binary strings is larger.
Decoders can be used to convert a binary code into a singular
active output representing its numeric value.
Encoders can be used to generate a coded output from a singular
active numeric input line.
Multiplexers are capable of funneling several data lines into a
single line for transmission to another point.
Demultiplexers are used to take a single data value or waveform
and route it to one of several outputs.
School of Engineering Technology and Applied Science (SETAS) /
Sustainable Design & Renewable Energy (SDRE)
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