# Introduction to Combinational Logic Circuits

The signals are usually represented by discrete bands of analog levels in digital electronic circuits or digital electronics instead of continuous ranges represented in analogue electronics. The simple electronic representations of Boolean logic functions, large assemblies of logic gates are typically used to make digital electronic circuits. In digital circuit theory, the circuits, thus formed from logic gates are used to generate outputs based on the input logic. Hence, these circuits are called as logic circuits and are classified into two types such as sequential logic and combinational logic circuits.

The logic gates can be defined as simple physical devices used to implement the Boolean function. Logic gates are used to perform a logical operation with one or more inputs and generates a logical output. These logic circuits are formed by connecting one or more logic gates together. These logic circuits are classified into two types: sequential logic circuits and combinational logic circuits.

## Combinational Logic Circuits

In this article, let us discuss about introduction to logic circuits, combinational logic circuits, combinational logic circuit definition, combinational logic circuit design, functions of combinational logic.

### Combinational Logic Circuit Definition

The combinational logic circuits or time-independent logic circuits in digital circuit theory can be defined as a type of digital logic circuit implemented using Boolean circuits, where the output of logic circuit is a pure function of the present inputs only. The combinational logic circuit operation is instantaneous and these circuits do not have the memory or feedback loops.

This combinational logic is in contrast compared to the sequential logic circuit in which the output depends on both present inputs and also on the previous inputs. Thus, we can say that combinational logic does not have memory, whereas sequential logic stores previous input in its memory. Hence, if the input of combinational logic circuit changes, then the output also changes.

### Combinational Logic Circuit Design

These combinational logic circuits are designed to produce specific outputs from certain inputs. The combinational logic design can be done using two methods such as a sum of products and a product of sums. Combinational logic circuits are generally designed by connecting together or combining the basic logic gates such as NAND, NOR, and NOT. Hence, these logic gates are termed as building blocks. These logic circuits can be a very simple circuit or a very complex circuit or huge combinational circuit can be designed using only universal logic gates such as NAND and NOR gates.

### Functions of Combinational Logic Circuit

The function of combinational logic circuits can be specified in three main ways such as:

- Truth Table
- Boolean Algebra
- Logic Diagram

#### Truth Table

The logic gate function can be defined using its truth table which consists outputs for of all possible combinations of inputs of the logic gate. An example combinational logic function truth table is shown in the above figure.

#### Boolean Algebra

The output of combinational logic function can be expressed in the form expression using Boolean algebra and an example, Boolean expression for the above truth table is shown in the above figure.

#### Logic Diagram

The graphical representation of combinational logic functions using logic gates is called as logic diagram. The logic diagram for above discussed logic function truth table and Boolean expression can be realized as shown in the above figure.

The combinational logic circuits can be also be called as decision making circuits, as these are designed using individual logic gates. The combinational logic is the process of combining logic gates to process the given two or more inputs such that to generate at least one output signal based on the logic function of each logic gate.

#### Classification of Combinational Logic

The combinational logic circuits can be classified into various types based on the purpose of usage, such as arithmetic & logical functions, data transmission, and code converters. To solve the arithmetic and logical functions we generally use adders, subtractors, and comparators which are generally realized by combining various logic gates called as combinational logic circuits. Similarly, for data transmission, we use multiplexers, demultiplexers, encoders, and decoders which are also realized using combinational logic. The code converters such as binary, BCD, and 7-segment are designed using various logic circuits.

In fact, combinational logic is most frequently used in multiplexer and demultiplexer type circuits. If multiple inputs or outputs are connected to the common signal line, then the logic gates are used for decoding an address in order to select single data input or output switch.

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