Combinational Logic

Definition of a Combinational Circuit

A combinational (logic) circuit in its most general form with m inputs and n outputs is shown symbolically in the figure above. We will assume for our discussion that each input line and each output line may carry signals that correspond to two states (two-valued or binary inputs), although if we wished to be more general we would have to allow for the possibility of each line's carrying signals having more than two states (multivalued logics). The two states might be electrically represented by

1. "high" or "low" voltage
2. grounded or ungrounded
3. pulse or no pulse
4. positive pulse or negative pulse, etc

The definition of a combinational circuit requires that the states of the output lines at any instant depend only on the states of the inputs at the same instant. That is, previous input states have no effect on present output states. Thus there are no memory elements in a combinational circuit. However, all physical devices used for constructing combinational circuits exhibit some time delay in their operation, and time delay has a memory function. Hence, when we use physical devices in combinational circuits we must be careful to understand the effect such time delays have on the circuits' behavior.

Combinational circuits can be divided into several categories. Examples are

1. multiplexers
2. demultiplexers
3. decoders
4. encoders
5. adders
6. subtractors