5.6
Multiplexer/Demultiplexer
In
the realm of digital electronics, multiplexers (Mux) and demultiplexers (Demux) are indispensable combinational logic circuits that play
a pivotal role in data routing, communication, and system design. Often
referred to as "data selectors" and "data distributors"
respectively, these devices enable the efficient management of information flow
by allowing multiple data streams to share a single transmission line, or
conversely, directing a single data stream to one of several destinations.
Their ability to dynamically control data paths makes them fundamental building
blocks in various applications, from telecommunications and computer memory
systems to complex data acquisition and processing units.
Part 5.6.1
Multiplexer
An MSI circuit capable of selecting a
single input from several inputs and routing the selected input to a single
output. The output line is connected to any of the input line depending on the
logic combinations at the select lines. It is also called a data selector.
Figure 1. Block
Diagram of a Multiplexer
Table 1. Function Table of Multiplexers
|
S1 |
S0 |
Y |
|
0 |
0 |
I0 |
|
0 |
1 |
I1 |
|
1 |
0 |
I2 |
|
1 |
1 |
I3 |
Figure 2. Logic
Circuit of 4x1 Multiplexer (from: Nigde University)
Part 5.6.1
.1Boolean Function Implementation using multiplexers
Steps:
1. Express the
Boolean function in SOP form.
2.
For n variables,
connect the n-1 variables to the selection lines.
3.
List the inputs
to the multiplexer and under them list the minterms
in two rows. The first row is with A complemented and the second row is with A
uncomplemented.
4.
Circle all the minterms of the function and apply the following:
a.) If two minterms
in a column are not circled, apply 0 to the corresponding multiplexer input.
b.) If the two minterms
are circled, apply 1 to the corresponding multiplexer input.
c.) If the bottom minterm
is circled and the top is not, apply A to the corresponding multiplexer input.
d.) If the top minterm
is circled and the bottom is not, apply A' to the corresponding multiplexer
input.
Example no. 1
Implement the following function with
a multiplexer.
F(A,B,C,D)=Σ(0,1,3,4,8,9,15)
Solution no. 1
Based on the given function which
involves four variables, a multiplexer with three selection lines and eight
inputs is needed. Applying B, C, and D to the selection lines and A to the minterms, the implementation table is shown as:
Example of a multiplexer IC is the
74x151 8-input, 1-bit multiplexer that comes in a 16-pin dual-in-line package.
Example no. 2
Implement F(A,B,C,D)=Σ(0,3,5,6,8,9,14,15)
Solution no. 2
Truth table:
|
A |
B |
C |
D |
F |
|
0 |
0 |
0 |
0 |
1 |
|
0 |
0 |
0 |
1 |
0 |
|
0 |
0 |
1 |
0 |
0 |
|
0 |
0 |
1 |
1 |
1 |
|
0 |
1 |
0 |
0 |
0 |
|
0 |
1 |
0 |
1 |
1 |
|
0 |
1 |
1 |
0 |
1 |
|
0 |
1 |
1 |
1 |
0 |
|
1 |
0 |
0 |
0 |
1 |
|
1 |
0 |
0 |
1 |
1 |
|
1 |
0 |
1 |
0 |
0 |
|
1 |
0 |
1 |
1 |
0 |
|
1 |
1 |
0 |
0 |
0 |
|
1 |
1 |
0 |
1 |
0 |
|
1 |
1 |
1 |
0 |
1 |
|
1 |
1 |
1 |
1 |
1 |
Implementation Table:
|
|
I0 |
I1 |
I2 |
I3 |
I4 |
I5 |
I6 |
I7 |
|
A’ |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
|
A |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
|
|
1 |
A |
0 |
A’ |
0 |
A’ |
1 |
A |
Schematic Diagram:
Part 5.6.2
Demultiplexer
A combinational circuit
that receives multiplexed information on a single line and transmits this
information on one of 2n possible output line. The selection of a
specific output line is controlled by the bit values of n selection lines.
A decoder with an
enable input can function as a demultiplexer.
Figure 3. Decoder
with enable pin
Figure 4.
Demultiplexer
Example IC is
74x155 which is a 2-bit, 4-output demultiplexer
|
E |
A |
B |
D0 |
D1 |
D2 |
D3 |
|
1 |
x |
X |
1 |
1 |
1 |
1 |
|
0 |
0 |
0 |
0 |
1 |
1 |
1 |
|
0 |
0 |
1 |
1 |
0 |
1 |
1 |
|
0 |
1 |
0 |
1 |
1 |
0 |
1 |
|
0 |
1 |
1 |
1 |
1 |
1 |
0 |
Figure 5. Logic
Circuit of IC 74x155