## Multiplexers

### Objective:

To design multiplexers and to study multiplexer chips and their applications

### Definition of a Multiplexer:

Figure 1 - A Multiplexer

A multiplexer is a combinational network with:

n control (or select) lines; C1, C2, ..., Cn
2n input lines; I0, I1, ...,I2n-1
One output line Z

A multiplexer selects binary information from one of 2n input lines and transmits it to a single output line. The selection of the particular input line is controlled by minterms of control lines. In general, the Boolean expression of the output is given by:

Equation 1

Where

Ij is the jth input
m0 = C'nC'n-1...C'2C'1
m1 = C'nC'n-1...C'2C1
m2 = C'nC'n-1...C2C'1
m2n-1 = CnCn-1...C2C1

For example, with three control lines, (C3, C2, C1), Equation 1 becomes

Equation 2

Further, when C3 = 1, C2 = 0 and C1 = 1, then I5 is selected since

m5 =1 and all mj = 0 for j= 0, l, 2, 3, 4, 6, 7

### Design Problems:

1. Design and wire up a 4 to 1 multiplexer. (You will need two select lines.) Demonstrate your circuit to your instructor.
2. The 74153 is a dual 4 to 1 multiplexer. Study its specifications and wire it up for an 8 to 1 multiplexer. Verify its operation and demonstrate the circuit to your instructor.
3. On one site there are four computers and about 200 yards away four output devices. It is required that each computer be able to output data to any of the four devices. To reduce the installation cost, only one data line will link the computers to the output devices. You are required to design the communication network. Draw the schematic diagram and wire it up on your breadboard. Assume that four switches are the computers and four led's are the output devices. Demonstrate your circuit to your instructor. (You will need both 74155 and 74153 chips.)
4. Using a minimum number of 74153 chips as 8 to 1 multiplexer, design (only on paper) a 16 to 1 multiplexer.