An adder is a logic circuit that can perform additional operations on binary numbers. It can be composed of only three types of logic circuits: AND, OR, and NOT gates.
Bit addition is handled with an XOR gate (a combination of NOT, AND, and OR gates), and carry that occurs when '1+1' is calculated is treated as an AND gate.
Half adder has only two inputs and there is no provision to add a carry coming from the lower order bits when multi addition is performed. It becomes a 'full adder' if it can handle up to the carrying of the lower order bit.
A half adder circuit implemented only with transistors on a breadboard