A binary adder is a digital circuit that performs the addition of binary numbers. It takes two binary inputs and produces a sum and a carry output. There are two main types of binary adders: the half adder, which adds two single bits, and the full adder, which adds three bits, including a carry from a previous addition. Binary adders are fundamental components in computer architecture and are used in arithmetic logic units (ALUs) to perform calculations. They enable various applications, from simple calculations in calculators to complex operations in processors, making them essential for digital computing.