1. Digital Design Module 2 Multiplexer and Demultiplexer
Amit Kumar AP
SCSE, GU Greater Noida

2. OUTLINE Introduction to Multiplexer
Implementation of 2x1, 4x1 and 8x1 Mux
Multiplexer with enable input
Cascading of Multiplexers
Combinational Logic Circuit Implementation using a Multiplexer
Introduction to De-multiplexer
Implementation of 1x4 De-Mux

3. Multiplexer (MUX)
A multiplexer can use addressing bits to select one of several input bits to be the output.
A selector chooses a single data input and passes it to the MUX output
It has one output selected at a time.

4. Cont..
A multiplexer has
N control inputs
2N data inputs
1 output
A multiplexer routes (or connects) the selected data input to the output.
The value of the control inputs determines the data input that is selected.

5. Block Diagram Select Lines Inputs Output 1 2N N MUX (sources)
(destination) 1 2N N
MUX

6. Typical Application of a MUX
Multiple Sources
Selector
Single Destination
MP3 Player
Docking Station
Surround Sound System
Laptop
Sound Card D0 D1 D2 D3
MUX Y
Digital
Satellite B A
Selected Source
MP3 1
Laptop
Satellite
Cable TV
Digital
Cable TV

7. 2-to-1 Multiplexer (MUX)
Data
inputs
Z = A′.I0 + A.I1
Control
input

8. 2x1 mux

9. 4-to-1 Multiplexer (MUX)D0 D1 D2 D3 Y
B A B A Y D0 1 D1 D2 D3

10. 4-to-1 Multiplexer (MUX)
MSB
LSB A B F I0 1 I1 I2 I3
Z = A′.B'.I0 + A'.B.I1 + A.B'.I2 + A.B.I3

11. 8-to-1 Multiplexer (MUX)
MSB
LSB A B C F I0 1 I1 I2 I3 I4 I5 I6 I7
Z = A′.B'.C'.I0 + A'.B'.C.I1 + A'.B.C'.I2 + A'.B.C.I3 +
A.B'.C'.I0 + A.B'.C.I1 + A'.B.C'.I2 + A.B.C.I3

12. Function table with enable12

13. Cascading multiplexers
Using three 2-1 MUX to make one 4-1 MUX F S1 S0 F I0 1 I1 I2 I3 13

15. 8-to-1 multiplexer using 2-to-1 multiplexers.
Example: Construct an
8-to-1 multiplexer using
2-to-1 multiplexers. I0 I1 S2 S1 S0 F I0 1 I1 I2 I3 I4 I5 I6 I7 I2 I3 F
2-1
MUX
S E I4 I5
S2 E I6 I7 15

16. 1.Express the function in its sum of minterms form.
Implementing Boolean functions with multiplexers
Any Boolean function of n variables can be implemented with 2n-1-to-1 multiplexer. The procedure for implementing a Boolean function with a multiplexer is
1.Express the function in its sum of minterms form.
2. Order the sequence of variables chosen for the minterms. Suppose the sequence is , where A is the leftmost variable, and are the remaining n-1 variables.

17. CONT…
3.Connect the n-1 variables to the selection lines of the 2n-1-to-1 multiplexer, with B connected to the highest order selection line, and so on.
4. Construct the implementation table: List all the minterms in two rows.
The first row consists of minterms 0 to 2n-1 -1 (in all of which A is complemented).
The second row consists of minterms 2n-1 to 2n-1 (in all of which A is uncomplemented). .

18. CONT..
5. Circle all the minterms of the function and inspect each column in the implementation table separately
If the two minterms in a column are not circled, apply 0 to the corresponding multiplexer input.
If the two minterms are circled, apply 1 to the corresponding multiplexer input.
If the bottom minterm is circled, and the top is not circled, apply A to the corresponding multiplexer input.
If the top minterm is circled but not the bottom, apply A*

20. Consider the function of 3 variables:
1. Input variables B and C are applied to the selection lines s1 and s0, respectively.
2. Construct the implementation table, and circle all the minterms of the function in the implementation table
3. Apply 0, 1, A, and    to the inputs I0 through I3.

21. Implementing a Boolean Function using a Multiplexer
G(x,y,z) = m( 1, 4, 5, 6 )

22. Multiplexer as a Full-Adder

23. De-Multiplexer (De-MUX)
A demultiplexer performs the opposite function of a multiplexer.
A DEMUX is a digital switch with a single input (source) and a multiple outputs (destinations).
The select lines determine which output the input is connected to.

24. Cont.. A demultiplexer has
N control inputs
1 data input
2N outputs
A demultiplexer routes (or connects) the data input to the selected output.
The value of the control inputs determines the output that is selected.

25. Block Diagram- De-Mux Select Lines Input Outputs 2N 1 N DEMUX (source)
(destinations) 2N 1 N
DEMUX

26. Typical Application of a DEMUX
Single Source
Selector
Multiple Destinations
B/W Laser
Printer
Fax
Machine D0 D1 D2 D3 X
DEMUX
Color Inkjet
Printer B A
Selected Destination
B/W Laser Printer 1
Fax Machine
Color Inkjet Printer
Pen Plotter
Pen
Plotter

27. 1-to-4 De-Multiplexer (DEMUX)
B A
DEMUX B A D0 D1 D2 D3 X 1
D0 = A'.B'.X
D1 = A.B'.X
D2 = A'.B.X
D3 = A.B.X