CS355 Sylabus

Many-to-one digital switching circuit: multiplexor

A multi-way switch or many-to-one switch is a device that allow you to make a selection from many input value:

The above figure shows the logical function of a many-to-one switch in 2 different state. In the left figure, the switch directs the top-most input to the output, and in the second, it directs the 3rd input to the output.
You are familiar with a multi-way switch, you find them in many common devices.
One example is the switch in a boom box that let you select from CD, radio, and cassete.
The many-to-one switch in computer is called a multiplexor or mux.
Schematically (functionally), a multiplexor looks like this:
- It has 2^N input signals
- It has N control signals
- It has 1 output signal
- The output signal is equal to one of the input signal depending on the current value of the control signals.
  The dependency is as follows:

The multiplexor can be constructed using a simple 2 staged technique.

In the first stage, we use 2^N and gates to filter out the desired input signal.
The and-gates must be connected in such a way that for any given combination of control signal, only the desired input signal is switch out, while all other input signal is cut off.
Example: N=2
In the second stage, we use one or gate to collect all the outputs from the and-gates.
Example:

Here is (again) the circuit diagram for a 4x1 multiplexor (4x1 means it switches 4 inputs to 1 output):
The following circuit diagram shows what will happen when the control signals are 11 (= 3_decimal)) (the mux will switch the input i3 to the output):
- Notice that three of the and gates will receive at least one input that is equal to ZERO (red line). These and-gates will output ZERO.
- Notice that the top-most and gates will receive all 1's from the control-inputs. The top-most and-gate will operate as a "pass-through" for the input signal i₃
- The output of the top-most and-gate is equal to the input value i₃
- Looking at the Or-gate, you will notice that all but one input is ZERO (because all but one and-gates in the first stage will output ZERO).
- The or-gate will thus also operate as a "pass-through" for the input signal i₃
The other cases of control signals are similar. For example, if the control signals are (0,0), then the top-most 3 and-gates will receive at least one input signal that is ZERO and will output ZERO. The bottom and-gate will operate as a "pass-through" for the input signal i₀ The or-gate will now operate as a "pass-through" for the input signal i₀
You can see the circuit in action with EDiSim yourself: click here
Run the mux circuit as:
In this circuit, I adding some probes to show the output values of the AND gates to show you how this circuit works:
Notice only the select input will pass through its AND-gate.
All the outputs of the non-selected AND-gates are equal to ZERO.