Digital Electronics Fundamentals: Combinational Logic

The BCD-to-7-Segment Decoder

 The BCD-to-7-
segment decoder
accepts the BCD code
on its inputs and
provides outputs to
drive 7-segment
display devices to
produce a decimal
readout.

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The BCD-to-7-Segment Decoder

(The Application)

Decoders

Application
 Decoders are used in computers for i/p and

o/p selection.
 Computers must communicate with variety

of devices such as printers, modems,
scanners, keyboard and other PC.
 Decoders is used to select the I/O port so,
data can be sent or received from that
devices.

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Encoders

 Performs a reverse decoder function.

Circuit that allows only one input to be
activated, and produces an N-bit output

code, depending on which input is activated.

 The process of converting from symbols or
numbers to a coded format is encoding.

The tips to remember how to use encoder

is : Decimal BCD (coded).

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Encoder

Example, as shown in figure below, the
encoder has 10 inputs and 4-bit output.
Input and output are ACTIVE HIGH.

S0 A
S1 B BCD
S2 C
D
Decimal-

to-BCD

S8 encoder
S9

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The Decimal-to-BCD Encoder

(The Application)

Encoder

 Truth table for Decimal-to-BCD encoder

S0 S1 S2 S3 S4 S5 S6 S7 S8 S9 A B C D
1 0000

1 0001
1 0010
1 0011
1 0100
1 0101
1 0110
1 0111
1 1000
1 1 0 0 1 25

Encoder

 The 74147 Decimal-to-BCD Priority Encoder.
 Active-LOW input, active-LOW output.
 BCD zero output means none of the inputs is

active.

26

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UNIT 5 :COMBINATIONAL LOGIC

MULTIPLEXERS &
DEMULTIPLEXERS

Learning Outcome

At the end of this class, students should be
able to:
 Identify the function of multiplexer and

demultiplexer

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Multiplexer (MUX)-Data Selector

 Device that allows digital data from several
sources to be routed onto a single line.

Basic MUX has several data-input lines and
a single output line.

 Data select input allows one of digital data
to be switched to the output line.

Known as data selector.

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2-to-1 Multiplexer

S Output (Z)

0 I0
1 I1

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Multiplexer (MUX)-Data Selector

A logic symbol for a 4-input MUX.

There are two data select lines because
with two select bits, any one of the four
data input lines can be selected.

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Multiplexer (MUX)-Data Selector

DATA-SELECT INPUT INPUT SELECTED

S1 S0 D0
00 D1
D2
01 D3

10

11

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Multiplexer (MUX)-Data Selector

Logic expression for the output.
 Data o/p is equal to D0 if S1=0 and S0=0

Y=D0 S1 S0

 Data o/p is equal to D1 if S1=0 and S0=1

Y=D1S1 S0

 Data o/p is equal to D2 if S1=1 and S0=0

Y=D 2S1 S0

 Data o/p is equal to D3 if S1=1 and S0=1

Y=D 3S1S0

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Multiplexer (MUX)-Data Selector

The total expression for the data output is

Y=D 0S1 S0  D1S1 S0  D 2S1 S0  D3S1S0

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Multiplexer (MUX)-Data Selector

Example:
Determine the o/p waveform.

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8 input Multiplexer -74LS151

Has 8 data input.
Has 3 data-select or address input line (S0-S2)

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8 input Multiplexer -74LS151

 This multiplexer has an enable input E and
provides both the normal and the inverted
outputs.

 When E=0, the select inputs S2S1S0 will
select one data input (from D0 through D7)
for passage to output Y.

  When E=1, the multiplexer is disabled so
that Y= 0 regardless of the select input
code.



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16 input Multiplexer -74LS151

Two 8-Input MUX can be combine to
produce 16-input MUX

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We can use 2-to-1 to implement 4-to-1
MUX. 3 units of 2-to-1 MUX are required.

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Exercise: Multiplexer

4 input multiplexer:
From the timing diagram below, find the
output waveform with the data input D0=0,
D1=1,D2=1,D3=0.

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Demultiplexer (DEMUX)

 Demux is reverses the multiplexing
function.

It takes information from one line and
distributes it to a given number of output
lines. (several lines)

 Demux can be known as data distributor.

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Demultiplexer (DEMUX)

A 1-line to 4-line Demux.
I0 is a data input. If I0 =0, all output 0. If I0 =1,

output depend on data select.

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Demultiplexer (DEMUX)

S1 S0 I0 Q3 Q2 Q1 Q0

00 0 0 0 0 0

00 1 0 0 0 1

01 0 0 0 0 0

01 1 0 0 1 0

10 0 0 0 0 0

10 1 0 1 0 0

11 0 0 0 0 0

11 1 1 0 0 0

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Demultiplexer (DEMUX)

Example: Determine data output waveforms.

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