1) A multiplexer is a combinational circuit with m inputs, n control inputs, and 1 output that can select one of the m inputs to pass to the output based on the values of the n control inputs. 2) A 4-to-1 multiplexer has 4 inputs, 2 control inputs, and 1 output. The output will be one of the 4 inputs depending on the binary values of the 2 control inputs. 3) A demultiplexer is the opposite of a multiplexer, taking a single input and distributing it to one of multiple outputs based on the control inputs. It can also be used as a decoder to output a binary word based on the control input code.

1. Example of a Combinatorial Circuit: A Multiplexer (MUX) Consider an integer ‘m’, which is constrained by the following relation: m = 2 n , where m and n are both integers. m=no of inputs n=no of control inputs A m-to-1 Multiplexer has m Inputs: I 0 , I 1 , I 2 , ................ I (m-1) one Output: Y n Control inputs: S 0 , S 1 , S 2 , ...... S (n-1) One (or more) Enable input(s) such that Y may be equal to one of the inputs, depending upon the control inputs.

2. Example: A 4-to-1 Multiplexer A 4-to-1 Multiplexer: I 0 I 1 I 2 I 3 S 0 S 1 Y 1 output n control inputs 2 n inputs Enable (G)

3. Characteristic Table of a Multiplexer If the MUX is enabled, s 0 s 1 0 0 Y=I 0 0 1 Y=I 1 1 0 Y=I 2 1 1 Y=I 3

4. Multiplexer: Example 1 using a 16-to-1 multiplexer: F I 0 0 0 1 0 I 1 I 2 I 3 I 4 I 5 I 8 I 6 I 9 I 7 I 11 I 10 I 13 I 12 I 14 I 15 0 0 0 0 1 1 1 1 1 1 1 1 S 3 S 2 S 1 S 0

5. Multiplexer: Example 2

6. Multiplexer: Example 3 Z X Y

7. Multiplexer: Example 4

8. Demultiplexer (DMUX)/ Decoder When used as a demux their basic function is to take a single line input and send it to one of the several outputs depending upon the value of selection inputs. When used as a decoder.Their basic function is to accept a binary word (code) as an input at the selection inputs and create a different binary word as an output .

9. The diagram below shows the relation between a multiplexer and a Demultiplexer . I0 I1 I2 I3 S1 S0 Y out Y0 Y1 Y2 Y4 S1 S0 Input 4 to 1 MUX 1 to 4 DEMUX

10. Characteristic table of the 1-to-4 DMUX : Table 1

11. A Decoder is a Demultiplexer with a change in the name of the inputs : When the IC is used as a Decoder, the input I is called an Enable input Y0 Y1 Y2 Y4 S1 S0 ENABLE INPUT 2 to 4 Decoder

12. Characteristic Table of a 2-to-4 DECODER, with ACTIVE LOW Outputs and with ACTIVE LOW Enable Input: Table 2