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Problem

Sum of Two Integers

LeetCode #371Medium
XOR sum + carry · add without +

Compute the sum a + b of two integers without using the + or − operators.

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XOR sum + carry
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1// a + b without + or −
2while b != 0:
3    carry ← (a & b) << 1   // overflow columns
4    a ← a ^ b              // sum without carry
5    b ← carry
6return a
state
  • a00011 = 3
  • b00101 = 5
  • rulesum = a^b, carry = (a&b)<<1

line 1Goal: a + b without + or −. Look at one column of binary addition: 0+0=0, 0+1=1, 1+0=1, 1+1=0 carry 1. Notice the result bit is exactly a ^ b (XOR), and a carry happens only where BOTH bits are 1 (a & b). So addition = XOR + carry, and we repeat until the carry is empty.