Post on 18-Jan-2018
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DKT 122/3DIGITAL SYSTEM 1
WEEK #8 FUNCTIONS OF COMBINATIONAL LOGIC
(ENCODER & DECODER, MUX & DEMUX)
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Topic Outlines
Encoder Decoder Multiplexers (MUX) Demultiplexers (DEMUX)
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Topic Outlines
Encoder Decoder Multiplexers (MUX) Demultiplexers (DEMUX)
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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
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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
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Draw a Truth-Table showing input and output
DECIMAL DIGIT
BCD CODEA3 A2 A1 A0
0 0 0 0 01 0 0 0 12 0 0 1 03 0 0 1 14 0 1 0 05 0 1 0 16 0 1 1 07 0 1 1 18 1 0 0 09 1 0 0 1
Encoder
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(b) From the Truth-Table, get the equation for each output:
A3= Σ m(8, 9) A2= Σ m(4, 5, 6, 7) A1= Σ m(2, 3, 6, 7) A0= Σ 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
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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
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Decoding logic for the binary code 1001 with an active-HIGH output.
Basic Binary DecoderExample: 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 inputcombinations, the output is 0
Decoder
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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
Decoding function,
A4
A2
A1
A0
A3
Decoder
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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
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3 to 8 Binary
Decoder
Question: Is this active-HIGH or active-LOW output?
Decoder
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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 don’t-cares
D C B A a b c d e f g0 0 0 0 1 1 1 1 1 1 00 0 0 1 0 1 1 0 0 0 00 0 1 0 1 1 0 1 1 0 10 0 1 1 1 1 1 1 0 0 10 1 0 0 0 1 1 0 0 1 10 1 0 1 1 0 1 1 0 1 10 1 1 0 0 0 1 1 1 1 10 1 1 1 1 1 1 0 0 0 01 0 0 0 1 1 1 1 1 1 11 0 0 1 1 1 1 0 0 1 11 0 1 0 0 0 0 1 1 0 11 0 1 1 0 0 1 1 0 0 11 1 0 0 0 1 0 0 0 1 11 1 0 1 1 0 0 1 0 1 11 1 1 0 0 0 0 1 1 1 11 1 1 1 0 0 0 0 0 0 0 --
don
’t c
are
inpu
ts --
Decoder
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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
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2:1 MUX
Logic circuit Truth-table
Multiplexers (MUX)
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DATA-SELECT INPUTS INPUT
SELECTEDS0 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 thatany one of the 4 data-input linescan be selected
4-to-1MUX
S0
ZD1
D0
S1
D3
D2
D0D1D2D3 S1 S0
Z
4:1 MUX
Multiplexers (MUX)
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Total expression for the data output is:
013012011010 SSDSSDSSDSSDY
Logic diagram for 4:1 MUX
4:1 MUX
Multiplexers (MUX)
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Question 3:Construct an 8:1 multiplexer using block diagram.
8 input lines means there must be 3 data select lines.
Multiplexers (MUX)
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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
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1:4 DEMUX
Demultiplexers (DEMUX)
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Question 4:Construct a 1:4 DEMUX using block diagram. Show the equivalent Truth-Table.
1-4DEMUX
S 0
I0Q1Q0
S 1
Q3Q2
1-4DEMUX
S 0
I0Q1Q0
S 1
Q3Q2
S0
S1 Q0
Q1
I0
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)
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