Author: M Abo Bakar Aslam

16x1 Multiplexer (MUX)

A 16x1 Multiplexer (MUX) is a combinational circuit that selects one of sixteen input signals and forwards it to a single output line. The selection is controlled by four selection lines.

1. Truth Table - 16x1 Multiplexer

Suppose inputs are Input-0 to Input-15 and selection lines are S3, S2, S1 and S0. The outputs are represented as out-0 to out-15.

Total Number of Rows = 2^(number of selection lines) = 2⁴ = 16

Inputs	S3	S2	S1	S0	Output
Input-0 ... Input-15	0	0	0	0	Input-0 → out-0
Input-0 ... Input-15	0	0	0	1	Input-1 → out-1
Input-0 ... Input-15	0	0	1	0	Input-2 → out-2
Input-0 ... Input-15	0	0	1	1	Input-3 → out-3
Input-0 ... Input-15	0	1	0	0	Input-4 → out-4
Input-0 ... Input-15	0	1	0	1	Input-5 → out-5
Input-0 ... Input-15	0	1	1	0	Input-6 → out-6
Input-0 ... Input-15	0	1	1	1	Input-7 → out-7
Input-0 ... Input-15	1	0	0	0	Input-8 → out-8
Input-0 ... Input-15	1	0	0	1	Input-9 → out-9
Input-0 ... Input-15	1	0	1	0	Input-10 → out-10
Input-0 ... Input-15	1	0	1	1	Input-11 → out-11
Input-0 ... Input-15	1	1	0	0	Input-12 → out-12
Input-0 ... Input-15	1	1	0	1	Input-13 → out-13
Input-0 ... Input-15	1	1	1	0	Input-14 → out-14
Input-0 ... Input-15	1	1	1	1	Input-15 → out-15

As the circuit becomes highly complex, it is practically implemented using smaller multiplexers such as 2x1, 4x1 and 8x1 MUX.

Building 16x1 MUX using 2x1 MUX

To construct a 16x1 MUX using only 2x1 MUX:

First layer: Combine inputs in pairs using 2x1 MUX → total 8 MUX
Second layer: Combine outputs of first layer → 4 MUX
Third layer: Combine outputs → 2 MUX
Final layer: Combine outputs → 1 MUX

Total 2x1 MUX required = 8 + 4 + 2 + 1 = 15

Block Diagram for 16x1 MUX using 2x1 MUX only - visualized by edu2skill.com — Figure 1: 16x1 MUX using only 2x1 MUX

Building 16x1 MUX using 4x1 MUX

To construct a 16x1 MUX using only 4x1 MUX:

First stage: Use 4 MUX (each handles 4 inputs)
Second stage: Use 1 MUX to select final output

Total 4x1 MUX required = 4 + 1 = 5

Selection Lines:

Lower-level MUX controlled by S1 and S0
Final MUX controlled by S3 and S2

Block Diagram for 16x1 MUX using 4x1 MUX - visualized by edu2skill.com — Figure 2: 16x1 MUX using 4x1 MUX

Building 16x1 MUX using both 8x1 and 2x1 MUX

To construct a 16x1 MUX using 8x1 MUX:

First stage: Use 2 MUX (each handles 8 inputs)
Second stage: Use 1 MUX to select final output

Total MUX required = 2 (8x1) + 1 (2x1) = 3

Selection Lines:

8x1 MUX controlled by S2, S1, S0
Final 2x1 MUX controlled by S3

Block Diagram for 16x1 MUX using both 8x1 and 2x1 MUX - visualized by edu2skill.com — Figure 3: 16x1 MUX using both 8x1 and 2x1 MUX

Building 16x1 MUX using Combination of 2x1 and 4x1 MUX

Block Diagram for 16x1 MUX using 2x1 and 4x1 MUX - visualized by edu2skill.com — Figure 4: 16x1 MUX using 2x1 and 4x1 MUX

Important Note

As the number of inputs increases, design complexity increases. Therefore, hierarchical design using smaller multiplexers is preferred in practical digital systems.