10 MuxDemux

Multiplexer (MUX)¶

also called as data selector

Combinational circuit

Digital switch

• \(2^n\) inputs
• 1 output
• \(n\) selection lines

Applications¶

1. servers
2. multiple devices are connected to just a single server
3. telecommunication

2-1 Mux¶

• 2 inputs
• 1 output
• 1 selection line

\(M = i_0 {s_0}' + i_1 s_0\)

4-1 Mux¶

• 4 inputs
• 1 output
• 2 selection lines

\(Y = i_0 {s_0}' {s_1}' + i_1 {s_0}' s_1 + i_2 s_0 {s_1}' + i_3 s_0 s_1\)

8-1 Mux¶

• 8 inputs
• 1 output
• 3 selection lines

16-1 Mux¶

• 16 inputs
• 1 output
• 4 selection lines

Simplifying mux¶

1. draw truth table
2. Choose variable(s) as selection lines
3. other variable(s) as mux i/p
4. write the function in terms of the mux i/p (easier than drawing kmap)

Building Mux using smaller¶

1. divide \(n_1\) by \(n_2\)
2. no of muxes = sum of quotients

positions of s1 and s2 are important

MSD will be the selection line for the last mux

4x1 using 2-1¶

8x1 using 2-1¶

8x1 using 4x1 and 2x1¶

two 4x1 and one 2x1

\(8/4 = 2; 2/2 = 1\)

16x1 using 4x1¶

Diagram¶

De-multiplexer (De-mux)¶

it is a digital switch with

1. 1 input
2. \(n\) selection lines
3. determines which output is connected to the input
4. \(2^n\) multiple outputs

1-2¶

\(D_0 = i {S_0}', D_1 = iS_0\)

1-4¶

\(D_0 = i {s_0}'{s_1}', D_1 = i{s_0}'s_1, D_2 = i s_0 {s_1}', D_3 = i s_0 s_1\)

Diagram¶

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