Digital Circuits and Systems Multiplexers Shankar Balachandran* - - PowerPoint PPT Presentation

Shankar Balachandran* Associate Professor, CSE Department Indian Institute of Technology Madras

*Currently a Visiting Professor at IIT Bombay

Digital Circuits and Systems

Spring 2015 Week 3 Module 14

Multiplexers

Multiplexers 2

Multiplexers

 Multiplexing means transmitting a large number of information

units over a smaller number of channels or lines.

 A digital multiplexer (MUX) selects binary information from one

• f many input lines and directs it to a single output line.

 Data selector (2n:1 MUX).  Inputs: 2n data inputs, n select lines.  Output: 1 data output line.

s1 s0 Out D0 1 D1 1 D2 1 1 D3 D0 D1

1

D2 D3

1 Out

s1 s0

s1 s0 (control)

D0 D1 D2 D3

Out

2:1 Mux

Multiplexers 3

(a) Graphical symbol f s w0 w1

1

(b) Truth table 1 f s w0 w1 f s w0 w1 (c) Sum-of-products circuit

Multiplexers 4

Internal Structure of a 4:1 MUX

 A 2n:1 MUX needs 2n, (n+1)-input AND gates for selection and a

2n-input OR gate to generate the final output.

  AND/OR logic structure

Closeness to Decoders

Multiplexers 5

En

D2 D3 D1 D0

Connect all the input lines of the multiplexer together (to make enable) and remove the OR gate to give you a decoder

Multiplexers 6

MUX Output Boolean Expression

 2:1 MUX  4:1 MUX  General expression for 2n : 1 MUX

1

D s D s Out    

3 1 2 1 1 1 1

D s s D s s D s s D s s Out        

 

minterm the is where

th

i m D m Out

i i i i

n

  

  1 2

Using 2:1 Muxes to Build a 4:1 Mux

Multiplexers 7

w w

1 1

w

2

w

3 1

f

1

s

1

s

Multiplexers 8

Practical Application of Multiplexers

x

1 1

x

2 1

s y

1

y

2

x

1

x

2

y

1

y

2

2x2 crossbar switch

s

Multiplexers 9

MUX Based Logic Design

 MUXes are sometimes called hardware look-up tables.  To implement an n-variable function using a 2n:1 MUX

 Use a 2n:1 MUX, connect n input variables to the n select lines

(in the correct MSB-LSB order).

 Wire MUX input Di to 1 if function includes minterm mi. All other

inputs are set to 0.

 Example: Implement the function

using a MUX of appropriate size.

   

  7 4 2 1 , , , c , b , a F

F

Multiplexers 10

MUX Based Logic

 Advantages:

 Easier to design combinational circuits.  Easier to debug circuits designed using multiplexers.

 Disadvantages:

 Multiplexers can become very large for a large number of inputs.

  Good for small circuits.  Normally, any function with more than 4 variable is

impractical for direct implementation (i.e., using a single large MUX).

 Use tree of small MUXes or using a variable as MUX data input or

Shannon’s Expansion Theorem for implementing large functions.

Multiplexers 11

Multiplexer Tree

 A larger MUX can be implemented using a tree of smaller

MUXes.

 Example: Implement the function using

smaller MUXes instead of one 8:1 MUX.

   

  7 4 2 1 , , , c , b , a F

End of Week 3: Module 14

Thank You

Multiplexers 12