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FUNCTIONS OF COMBINATIONAL LOGIC
(ENCODER & DECODER, MUX & DEMUX)
Lecture 7
Digital Design
Dr. PO Kimtho
Department of Computer Sciences
Norton University (NU)
Topic Outlines
Encoder
Decoder
Multiplexers (MUX)
Demultiplexers (DEMUX)
Topic Outlines
Encoder
Decoder
Multiplexers (MUX)
Demultiplexers (DEMUX)
Encoder
Encoder converts information such as decimal number, alphabetical character, or symbols into some coded form, such as BCD or binary
Encoder is usually used for: Data representation Data security
Question 1:
Design a Decimal to BCD Encoder
Hints: (a) Draw a Truth-Table showing input and output - How many inputs? : 10 (0 to 9) - How many outputs? : 4 because we need 4 bits to express 9 (1001) (b) From the Truth-Table, get the equation for each
output - How many Boolean expression? : 4 since there are 4 outputs (c) Based on the output equation, draw a circuit for
basic decimal-to-BCD encoder
Encoder
Draw a Truth-Table showing input and output
DECIMAL DIGIT
BCD CODE
A3 A2 A1 A0
0 0 0 0 0
1 0 0 0 1
2 0 0 1 0
3 0 0 1 1
4 0 1 0 0
5 0 1 0 1
6 0 1 1 0
7 0 1 1 1
8 1 0 0 0
9 1 0 0 1
Encoder
(b) From the Truth-Table, get the equation for each output:
A3= m(8, 9) A2= m(4, 5, 6, 7) A1= m(2, 3, 6, 7) A0= m(1, 3, 5, 7, 9) (c) Based on the output
equation, draw a circuit for basic decimal-to-BCD encoder
(a) Logic symbol for a 10-line-to 4 line encoder
(b) Logic diagram. A 0-digit input is not needed because the BCD outputs are all low when there are no HIGH inputs
(a)
(b)
Encoder
A decoder is a circuit that creates an output based on the binary states of a given input
Do the opposite of encoder
Decoder
Decoder block diagram
Decoding logic for the binary code 1001 with an active-HIGH output.
Basic Binary Decoder
Example: To determine when a binary 1001 occurs on the input of a
digital circuit, AND gate can be used as the basic decoding element.
AND gate -> produce HIGH output when all inputs are HIGH How to ensure that inputs to the AND gate are HIGH when
binary 1001 occurs?
Other than this input
combinations, the
output is 0
Decoder
Question 2:
(a) Determine the logic required to decode the binary 11100 by producing a high level (active-HIGH) on the output.
Active-HIGH produce HIGH output
01234, AAAAAXnctionDecodingfu
Decoding function,
A4
A2
A1
A0
A3
Decoder
4-bit Decoder
This type of decoder is called 4-line-to-16-line decoder or 1-of-16 decoder
For a 4-bit decoder, there are 16 possible combinations (24=16). This means that 16 decoding gates are required
Decoder
3 to 8 Binary
Decoder
Question: Is this active-HIGH or active-LOW output?
Decoder
Example:
Seven Segment Decoder
A seven segment decoder has 4-bit BCD input and the seven segment display code as its output:
In minimizing the circuits for the segment outputs all non-decimal input combinations (1010, 1011, 1100,1101, 1110, 1111) are taken as dont-cares
D C B A a b c d e f g
0 0 0 0 1 1 1 1 1 1 0
0 0 0 1 0 1 1 0 0 0 0
0 0 1 0 1 1 0 1 1 0 1
0 0 1 1 1 1 1 1 0 0 1
0 1 0 0 0 1 1 0 0 1 1
0 1 0 1 1 0 1 1 0 1 1
0 1 1 0 0 0 1 1 1 1 1
0 1 1 1 1 1 1 0 0 0 0
1 0 0 0 1 1 1 1 1 1 1
1 0 0 1 1 1 1 0 0 1 1
1 0 1 0 0 0 0 1 1 0 1
1 0 1 1 0 0 1 1 0 0 1
1 1 0 0 0 1 0 0 0 1 1
1 1 0 1 1 0 0 1 0 1 1
1 1 1 0 0 0 0 1 1 1 1
1 1 1 1 0 0 0 0 0 0 0
-- d
on
t c
are
in
pu
ts -
-
Decoder
Multiplexers (MUX)
MUX is a device that allows digital information from several sources to be routed onto a single line for transmission
It is made up of several data-input lines and a single output line. It also has data-select inputs which permits digital data on any one of the inputs to be switched to the output line.
MUX is also known as data selectors
Logic symbol for a 4-input multiplexer (4:1 MUX)
n select inputs
1 data output
2n data inputs
2:1 MUX
Logic circuit Truth-table
Multiplexers (MUX)
DATA-SELECT INPUTS INPUT
SELECTED S0 S1
0 0 D0
0 1 D1
1 0 D2
1 1 D3
If a binary 0 (S0=0 and S1=0) is applied to the data-select lines, the data on input D0 appear on the data-output line
2 data-select lines means that
any one of the 4 data-input lines
can be selected
4-to-1
MUX
S0
Z D1
D0
S1
D3
D2
D0 D1
D2
D3 S1 S0
Z
4:1 MUX
Multiplexers (MUX)
Total expression for the data output is:
013012011010 SSDSSDSSDSSDY
Logic diagram for 4:1 MUX
4:1 MUX
Multiplexers (MUX)
Question 3:
Construct an 8:1 multiplexer using block diagram.
8 input lines means there must be 3 data select lines.
Multiplexers (MUX)
Demultiplexers (DEMUX)
DEMUX reverse the multiplexing functions
It takes digital information from one line and distributes it to a given number of output lines
DEMUX is also known as data distributor
1-line to 4-line DEMUX
1 data input
n select inputs
2n data outputs
1:4 DEMUX
Demultiplexers (DEMUX)
Question 4:
Construct a 1:4 DEMUX using block diagram. Show the equivalent Truth-Table.
1 - 4
DEMUX
S 0
I 0 Q 1
Q 0
S 1
Q 3
Q 2
1 - 4
DEMUX
S 0
I 0 Q 1
Q 0
S 1
Q 3
Q 2
S0
S1 Q0
Q1
I 0
Q2
Q3
S1 S0 I1 Q3 Q2 Q1 Q0
0 0 1 0 0 0 1
0 1 1 0 0 1 0
1 0 1 0 1 0 0
1 1 1 1 0 0 0
Truth-table
Block diagram
Logic circuit
Demultiplexers (DEMUX)
