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

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

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.

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.

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

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

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

2x1 mux

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

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

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

Function table with enable 12

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

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

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.

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). .

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*

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.

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

Multiplexer as a Full-Adder

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.

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.

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

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

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