binaryAdd

binaryAdd is a function or operation that computes the sum of two binary numbers, typically provided as strings of 0s and 1s or as bit arrays. It returns the binary representation of their sum. In software libraries, binaryAdd(a, b) may assume non-negative inputs represented in binary form; in other contexts it can operate on fixed-length bitsets or binary strings with or without leading zeros.

Operation: The standard approach processes bits from least significant to most significant, maintaining a carry. For each position i, sum = a_i + b_i + carry; result_i = sum mod 2; carry = floor(sum / 2). After processing all bits, if carry remains, it is appended as the most significant bit. The function can return the result as a string or as a bit array and may preserve or strip leading zeros according to the use case.

Complexity: Time complexity is linear in the length of the inputs, O(n), and space complexity is O(n) for the resulting value. If inputs are fixed-length, the maximum length grows by at most one bit due to the final carry.

Variations and implementation notes: Some versions accept integer inputs and convert to binary internally. In digital circuit design, a binaryAdd corresponds to a ripple-carry adder or to optimizations such as carry-lookahead adders. In software, implementations may optimize with bitwise operations or rely on language-provided arbitrary-precision integers.

Edge cases: Unequal lengths are handled by treating missing bits as zero. Non-binary characters should trigger validation errors. For signed numbers using two's complement representation, binaryAdd may require additional logic to handle sign bits or to constrain results.

See also: binary subtraction, two's complement, ripple-carry adder, carry-lookahead adder.