Multiplexer
A
multiplexer is a combinational circuit that has 2n input lines
and a single output line. Simply, the multiplexer is a multi-input and
single-output combinational circuit. The binary information is received from
the input lines and directed to the output line. On the basis of the values of
the selection lines, one of these data inputs will be connected to the output.
Unlike
encoder and decoder, there are n selection lines and 2n input
lines. So, there is a total of 2N possible combinations of
inputs. A multiplexer is also treated as Mux.
There
are various types of the multiplexer which are as follows:
2×1 Multiplexer:
In
2×1 multiplexer, there are only two inputs, i.e., A0 and A1,
1 selection line, i.e., S0 and single outputs, i.e., Y. On the
basis of the combination of inputs which are present at the selection line S0,
one of these 2 inputs will be connected to the output. The block diagram and
the truth table of the 2×1 multiplexer are given below.
Block Diagram: Truth Table :
The
logical expression of the term Y is as follows:
Y=S0'.A0+S0.A1
Logical
circuit of the above expression is given below:
4×1 Multiplexer:
In
the 4×1 multiplexer, there is a total of four inputs, i.e., A0, A1,
A2, and A3, 2 selection lines, i.e., S0 and
S1 and single output, i.e., Y. On the basis of the combination
of inputs that are present at the selection lines S0 and S1,
one of these 4 inputs are connected to the output. The block diagram and the
truth table of the 4×1 multiplexer are given below.
Block Diagram: Truth Table :
The
logical expression of the term Y is as follows:
Y=S1'
S0' A0+S1' S0 A1+S1 S0'
A2+S1 S0 A3
Logical
circuit of the above expression is given below:
8 to 1 Multiplexer
In
the 8 to 1 multiplexer, there are total eight inputs, i.e., A0, A1,
A2, A3, A4, A5, A6, and
A7, 3 selection lines, i.e., S0, S1and S2 and
single output, i.e., Y. On the basis of the combination of inputs that are
present at the selection lines S0, S1, and S2,
one of these 8 inputs are connected to the output. The block diagram and the
truth table of the 8×1 multiplexer are given below.
Block Diagram: Truth Table :
The
logical expression of the term Y is as follows:
Y=S0'.S1'.S2'.A0+S0.S1'.S2'.A1+S0'.S1.S2'.A2+S0.S1.S2'.A3+S0'.S1'.S2 A4+S0.S1'.S2 A5+S0'.S1.S2 .A6+S0.S1.S3.A7
Logical
circuit of the above expression is given below:
8 ×1 multiplexer using 4×1 and 2×1 multiplexer
We
can implement the 8×1 multiplexer using a lower order multiplexer. To
implement the 8×1 multiplexer, we need two 4×1 multiplexers and
one 2×1 multiplexer. The 4×1 multiplexer has 2 selection lines, 4
inputs, and 1 output. The 2×1 multiplexer has only 1 selection line.
For
getting 8 data inputs, we need two 4×1 multiplexers. The 4×1
multiplexer produces one output. So, in order to get the final output, we need
a 2×1 multiplexer. The block diagram of 8×1 multiplexer using 4×1
and 2×1 multiplexer is given below.
16 to 1 Multiplexer
In
the 16 to 1 multiplexer, there are total of 16 inputs, i.e., A0, A1,
…, A16, 4 selection lines, i.e., S0, S1, S2,
and S3 and single output, i.e., Y. On the basis of the
combination of inputs that are present at the selection lines S0, S1,
and S2, one of these 16 inputs will be connected to the output. The
block diagram and the truth table of the 16×1
Block Diagram: Truth Table :
The
logical expression of the term Y is as follows:
Y=A0.S0'.S1'.S2'.S3'+A1.S0'.S1'.S2 '.S3+A2.S0'.S1'.S2.S3'+A3.S0'.S1 '.S2.S3+A4.S0'.S1.S2'.S3'+A5.S0 '.S1.S2'.S3+A6.S1.S2.S3'+A7.S0 '.S1.S2.S3+A8.S0.S1'.S2'.S3'+A9 .S0.S1'.S2'.S3+Y10.S0.S1'.S2.S3 '+A11.S0.S1'.S2.S3+A12
S0.S1.S2 '.S3'+A13.S0.S1.S2'.S3+A14.S0.S1 .S2.S3'+A15.S0.S1.S2'.S3
Logical
circuit of the above expression is given below:
16×1 multiplexer using 8×1 and 2×1 multiplexer
We
can implement the 16×1 multiplexer using a lower order multiplexer. To
implement the 8×1 multiplexer, we need two 8×1 multiplexers and
one 2×1 multiplexer. The 8×1 multiplexer has 3 selection lines, 4
inputs, and 1 output. The 2×1 multiplexer has only 1 selection line.
For
getting 16 data inputs, we need two 8 ×1 multiplexers. The 8×1
multiplexer produces one output. So, in order to get the final output, we need
a 2×1 multiplexer. The block diagram of 16×1 multiplexer using 8×1
and 2×1 multiplexer is given below.
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