Note that In fact, we have
This fact is useful in performing integer division. We can compute divided by by recursion (note the summation sign above). Consider , we have
Since , , if is a power of 2, we can perform the div and mod operations by bit shift.
def div(m, n): # n+1 is 2^k assumed here result = 0 A = m while (True): A = A >> k B = A & n result = add(result, A) if A <= n: break if A == n: result = result + 1 return result def add(A, B): result = A XOR B carry = (A AND B) << 1 return add(result, carry) if carry else result