A half-adder is an arithmetic circuit that adds two binary digits, producing a sum bit and a carry bit. It is a basic building block for larger arithmetic circuits such as full-adders and multi-bit adders.

Let's break down the components and functioning of a half-adder:

Components of a Half-Adder:
1. Two inputs: The half-adder takes in two binary digits (0 or 1) as inputs. These digits represent the bits to be added.
2. Sum output: The half-adder produces a sum bit as an output, which represents the result of adding the two input bits.
3. Carry output: The half-adder also produces a carry bit as an output, which represents the carry generated during the addition.

Functioning of a Half-Adder:
1. Sum calculation: The sum bit is calculated by performing an XOR (exclusive OR) operation on the two input bits. If the two input bits are different, the sum bit is set to 1; otherwise, it is set to 0.
2. Carry calculation: The carry bit is calculated by performing an AND operation on the two input bits. If both input bits are set to 1, a carry is generated and the carry bit is set to 1; otherwise, it is set to 0.

The half-adder circuit is derived from basic logic gates such as XOR and AND gates. It can be implemented using various electronic components, such as transistors or integrated circuits.

Applications of Half-Adders:
1. Ripple carry adder: Multiple half-adders can be cascaded together to form a larger adder known as a ripple carry adder. This allows for the addition of multi-bit binary numbers.
2. Arithmetic logic units (ALUs): Half-adders are used as components in ALUs, which are responsible for performing arithmetic and logical operations in microprocessors and digital systems.

In conclusion, a half-adder is an arithmetic circuit that adds two binary digits, producing a sum bit and a carry bit. It is a fundamental building block for more complex arithmetic circuits and finds applications in various digital systems.