Summation without + operator in python

Question

Need to get sum of x and y without + operator.

I trid to sum two number using adder.If we xor x and y ( x ^ y ), we will get summation without carry. From x & y we can get carry. To add this carry in summation, call add function again. but its not give answer. where is the error in my code.

def add(a,b):
    if a == 0:
        return b
    return add(a^b, a&b)

x = 10
y = 20
print(add(10, 20))

Error:

File "main.py", line 4, in add

return add(a^b, a&b) File "main.py", line 4, in add return add(a^b, a&b) File "main.py", line 4, in add return add(a^b, a&b) File "main.py", line 4, in add return add(a^b, a&b) File "main.py", line 4, in add return add(a^b, a&b) File "main.py", line 4, in add return add(a^b, a&b) File "main.py", line 4, in add return add(a^b, a&b) File "main.py", line 4, in add return add(a^b, a&b) File "main.py", line 4, in add return add(a^b, a&b) File "main.py", line 2, in add if a == 0: RuntimeError: maximum recursion depth exceeded in comparison

Answer 1

You also have to shift the carries:

def add(a,b):
    if a == 0:
        return b
    if b == 0:
        return a
    return add(a^b, (a&b) << 1)

x = 3
y = 2
print(add(x, y))
# 5

Answer 2

This explains only why you end in an endless loop. Your proposed addition algorithm is flawed, see Thierry Lathuille 's answer for a correct addition as well.

---

You forgot half of the base case:

def add(a,b):
    if a == 0 or b==0:   # if either one is zero
        return a or b         # return the non-zero one (or 0 if both are 0)
    return add(a^b, a&b)

x = 10
y = 20
print(add(10, 20))

prints

30     # this only works for some numbers, you algo is not correct, try add(3,2)

---

Debugging:

def add(a,b):
    print(f"a  {bin(a):>10}")
    print(f"b  {bin(b):>10}")
    if a == 0 or b==0:
        return a or b
    return add(a^b, a&b)

a      0b1010
b     0b10100
-------------        # manually added the xor/and
xor     11110        # to show what happens:
and     00000        # b is 0       

a     0b11110
b         0b0        # now it terminates as b is 0

Answer 3

You missed two condition. If b == 0 then return a. Then also shift carry.

def add(a,b):
    if a == 0:
        return b
    if b == 0:
        return a
    return add(a^b, a&b << 1)

x = 10
y = 20
print(add(10, 20))