Algorithm 2 Adding Binary Integers
Input: A[1..n]A[1..n]A[1..n] and B[1..n]B[1..n]B[1..n] representing two n-bit binary numbers aaa and bbb.
Output: C[1..n+1]C[1..n+1]C[1..n+1] representing the result of a+ba + ba+b .
1:carry=0carry = 0carry=0
2:for i=ni = ni=n downto 111 do
3:C[i+1]=(A[i]+B[i]+carry) mod 2C[i + 1] = (A[i] + B[i] + carry) \bmod 2C[i+1]=(A[i]+B[i]+carry)mod2
4:if A[i]+B[i]+carry≥2A[i] + B[i] + carry \ge 2A[i]+B[i]+carry≥2 then
5:carry=1carry = 1carry=1
6:else
7:carry=0carry = 0carry=0
8:end if
9:end for
10:C[1]=carryC[1] = carryC[1]=carry