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. The simplest form is the Half Adder, which adds two single bits and outputs a sum and a carry bit. For adding larger binary numbers, a Full Adder is used, which can handle carry inputs from previous additions. Binary adders are fundamental components in computer architecture and are used in various applications, including arithmetic logic units (ALUs) and calculators. They enable efficient calculations in digital systems by processing binary data, which is the basis of all modern computing.