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 2N 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.

Examples:

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

• In the first stage, we use 2N 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.
• In the second state, we use one or gate to collect all the outputs from the and-gates.
• Here is the circuit diagram for a 4-way multiplexor:

• The following circuit diagram shows what will happen when the control signals are 11 (the mux will switch the top-most input 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 logic-sim yourself: click here