5.1 Combinational Logic Circuit

Part 5.1.1 Difference between Combinational circuits and Sequential circuits

Combinational circuits are characterized by outputs that are directly determined by the current inputs, without any reliance on past inputs. They implement specific information-processing operations using Boolean functions.

Sequential circuits, on the other hand, include memory elements (binary cells). Their outputs depend not only on the current inputs but also on the past state of these memory elements. This means their behavior is influenced by a time sequence of inputs and internal states. Sequential circuits are further elaborated in the next chapter.

The current chapter aims to use the knowledge from previous chapters to develop systematic design and analysis procedures for combinational circuits.

Figure 1. Simple Block Diagram of a Combinational Logic Circuit

A combinational circuit is made up of input and output variables connected by logic gates. These gates take in binary signals from the inputs and transform them into binary output signals, effectively converting input data into desired output data. Both input and output data are represented by binary signals, which can be either a logic-1 or a logic-0.

Figure 1 illustrates a typical combinational circuit. It receives 'n' binary input variables from an external source and sends 'm' output variables to an external destination. Often, these sources or destinations are storage registers, which can be close to the circuit or on a separate device. Crucially, these external registers do not affect the combinational circuit's operation; if they did, the entire system would be considered a sequential circuit.

With 'n' input variables, there are 2ⁿ possible input combinations. For each of these combinations, there is a unique output combination. A combinational circuit's behavior can be described by 'm' Boolean functions, with each function representing one output variable and expressed using the 'n' input variables.

Each input variable to a combinational circuit can be supplied via one or two wires. If only one wire is used, it might represent the variable in its normal (unprimed) or complemented (primed) form. If a Boolean expression requires a literal that isn't directly available from a single input wire, an inverter is needed to produce its complement. However, if an input variable is provided through two wires (one for the normal form and one for the complement), inverters are not necessary for that input. Most digital systems use flip-flop circuits as binary cells, which inherently provide both the normal and complemented values of a stored binary variable. For the remainder of our discussion, we will assume that each input variable is supplied with both its normal and complemented values simultaneously via two wires. Nevertheless, it's important to remember that an inverter can always be used to generate the complement if only a single wire input is available.