46. Half Adder Design

• Output Sum Analysis: The Sum channel is high only when a single input is active (rows 01 and 10), which directly matches an exclusive-OR (XOR) operation.
• Output Carry Analysis: The Carry channel is high only when both inputs are active simultaneously (row 11), which directly matches a logical AND operation.
• Hardware Optimization: Input A and Input B are routed in parallel to both gate blocks, enabling the circuit to calculate both arithmetic streams concurrently using a minimal two-gate footprint.
• Boolean Equations:

Output Sum = Input A ^ Input B

Output Carry = Input A . Input B