## Combinational Logic Functions

Read this chapter, which describes the design of several components using logic gates, including adders, encoders and decoders, multiplexers, and demultiplexers. This chapter also mentions ladder logic. If you are not familiar with ladder logic, you may also optionally read Chapter 6.1 and 6.2 as a reference. Note that ladder logic is not generally used in computer design and may be omitted. For the one input decoder, note that for a 0 input, the D0 output is a 1 and when the input is a 1, the D1 output is a 1. All the other decoders work the same way. One output line is a 1and the rest are 0's, indicating which binary number has been placed on the input lines. So an input in binary of the number 6 would cause D6 to be a 1.

### Demultiplexers

A demultiplexer, sometimes abbreviated dmux, is a circuit that has one input and more than one output. It is used when a circuit wishes to send a signal to one of many devices. This description sounds similar to the description given for a decoder, but a decoder is used to select among many devices while a demultiplexer is used to send a signal among many devices.

A demultiplexer is used often enough that it has its own schematic symbol

The truth table for a 1-to-2 demultiplexer is

Using our 1-to-2 decoder as part of the circuit, we can express this circuit easily

This circuit can be expanded two different ways. You can increase the number of signals that get transmitted, or you can increase the number of inputs that get passed through. To increase the number of inputs that get passed through just requires a larger line decoder. Increasing the number of signals that get transmitted is even easier.

As an example, a device that passes one set of two signals among four signals is a “two-bit 1-to-2 demultiplexer”. Its circuit is

or by expressing the circuit as

shows that it could be two one-bit 1-to-2 demultiplexers without changing its expected behavior.

A 1-to-4 demultiplexer can easily be built from 1-to-2 demultiplexers as follows.