Consider the binary numbers when they are in signed-2's complement representation. Each number has n bits: one for the sign and k = n - 1 for the magnitude. A negative number -X is represented as 2^k + (2^k - X), where the first 2^k designates the sign bit and (2^k - X) is the 2's complement of X. A positive number is represented as 0 + X, where the 0 designates the sign bit, and X, the k-bit magnitude. Using these generalized symbols, provethat the sum (±X) + (±Y) can be formed by adding the numbers including their sign bits and discarding the carry-out of the sign-bit position. In other words, prove the algorithm for adding two binary numbers in signed-2's complement representation.