The Multiplexers

        Multiplexing is the generic term used to describe the operation of sending one or more signals over a common transmission line at different times and as such, the device we use to do just that is called a Multiplexer.

A multiplexer is a combinational logic circuit design to switch one of several input lines through to one single output line by the application of a control signal. Multiplexers, often shortened to MUX, can be either digital circuits made from high speed logic gates used to switch digital or binary data or they can be analogue using transistors, mosfets or relays to switch one of the voltage or current inputs through to a single output.

Multiplexers also known as selectors because they can “select” each input line, are combinational logic circuits whose output condition either “HIGH” or “LOW” is determined at any time by its input state. In other words, multiplexers are switching circuits that just switch or route signals through themselves, and being a combinational circuit are memoryless as there is no signal feedback path.

The most basic type of multiplexer device is that of a one-way rotary switch as shown.

The rotary switch, also called a wafer switch as each layer of the switch is known as a wafer, is a mechanical device whose input is selected by rotating a shaft. In other words, the rotary switch is a manual switch that you can use to select individual data or signal lines simply by turning its inputs “ON” or “OFF”. So how can we select each data input automatically using a digital device.

The selection of each input line in a multiplexer is contro1led by an additional set of inputs called control lines. Normally, a multiplexer has 2^N input lines and a set of n control or address lines are needed to select one of the 2^N inputs to pass the data to the single output. Note that multiplexers are different in operation to Encoders. Encoders are able to switch an n-bit input pattern to multiple output lines that represent the binary coded (BCD) output equivalent of the active input.

We can build a simple 2-line to 1-line (2-to-1) multiplexer from basic logic NAND gates as shown.

2-input Multiplexer Design

The input A of this simple 2-1 line multiplexer circuit constructed from standard NAND gates acts to control which input ( I₀ or I₁ ) gets passed to the output at Q.

From the truth table we can see that when data select input, A is LOW (logic 0), input I₁ passes its data to the output while input I₀ is blocked. When data select A is HIGH (logic 1), input I₀ is passed to Q while input I₀ is blocked.

So by the application of either a logic “0″ or a logic “1″ at Q we can select the appropriate input with the circuit acting a bit like a single pole double throw (SPDT) switch. Then in this simple example, the 2-input multiplexer connects one of two 1-bit sources to a common output, producing a 2-to-1-line multiplexer and we can confirm this in the following Boolean expression.

Q = A.I₀.I₁ + A.I₀.I₁ + A.I₀.I₁ + A.I₀.I₁

and for our 2-input multiplexer circuit above, this can be simplified too:

Q = A.I₁ + A.I₀

We can increase the number of data inputs to be selected further simply by following the same procedure and larger multiplexer circuits can be implemented using smaller 2-to-1 multiplexers as building blocks. For a 4-input multiplexer we would therefore require two data select lines as 4-inputs represents 2² data control lines give a circuit with four inputs, I₀, I₁, I₂, I₃ and two data select lines A and B as shown.

4-input Multiplexer Design

 

We can see from above that the input which appears at the output Q is the only one selected by the control inputs A and B. The x value in the truth table corresponds to a “don’t care” condition. This means that the particular input can be at either a logic “0″ or a logic “1″ having no effect on the output state.

Then we can show the selection of the data through the 4-input multiplexer as a function of the data select bits as shown.

Adding more control address lines will allow the multiplexer to control more inputs by a value of 2ⁿ control lines, but each control line configuration will connect only ONE input to the output.

The Multiplexer is a very useful combinational logic device allowing multiple data lines to be connected to a single output and as such they can be used in many different applications such as signal routing, data communications and data bus control. In general, a multiplexer with n select lines can select one of 2ⁿ data inputs. Therefore, multiplexers are sometimes referred to as “data selectors”.