Combinational Circuit

A combinational circuit is a type of digital circuit that consists of logic gates and performs a specific Boolean function. It has no memory elements, which means that the output of the circuit depends solely on the current input values and not on any previous inputs or the circuit's history.

Half Adder

A half adder is a basic digital circuit that performs addition on two binary digits. It takes two inputs, A and B, and produces two outputs, the sum (S) and the carry (C). The sum output represents the least significant bit of the addition, while the carry output represents the most significant bit.

Working Principle

The half adder circuit consists of two logic gates: an XOR gate and an AND gate. The XOR gate computes the sum output, while the AND gate computes the carry output. The truth table for a half adder is as follows:

| A | B | S | C |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |

From the truth table, we can see that the sum output (S) is the result of the XOR gate, while the carry output (C) is the result of the AND gate.

Why is it a Combinational Circuit?

A half adder is a combinational circuit because it does not have any memory elements. The outputs (S and C) are solely determined by the current inputs (A and B) and do not depend on any previous inputs or the circuit's history. In other words, the output values are determined immediately based on the current input values.

Other Options

A sequential circuit is a type of digital circuit that has memory elements, such as flip-flops, and the output depends not only on the current input values but also on the previous input values and the circuit's history. Since a half adder does not have memory elements, it cannot be classified as a sequential circuit.

An asynchronous circuit is a type of digital circuit that does not rely on a clock signal for its operation. It operates based on the completion of individual logic functions and can have complex timing dependencies. A half adder, on the other hand, does not have any timing dependencies and operates solely based on the input values. Therefore, it is not an asynchronous circuit.

Hence, the correct answer is option A - a half adder is an example of a combinational circuit.