Sum of Two Integers Without + or -
A medium Bit Manipulation problem included in Love Babbar 450, Striver A2Z. Below: the roles whose interviews prioritise this topic, and how to practise it.
- Topic
- Bit Manipulation
- Sheets
- 2
- Core for
- 9 roles
- Platform
- LeetCode
The problem
Given two integers a and b, return their sum without using the + or - operators. Use bitwise operations to compute the sum.
Example 1
- Input
- a = 1, b = 2
- Output
- 3
- Why
- 1 + 2 = 3. Computed using XOR for sum without carry and AND with left shift for carry.
Example 2
- Input
- a = 2, b = 3
- Output
- 5
- Why
- 2 + 3 = 5. The XOR gives 1 and the carry gives 4, totaling 5.
Example 3
- Input
- a = -2, b = 3
- Output
- 1
- Why
- -2 + 3 = 1. The bitwise addition handles negative numbers correctly when using two's complement representation.
Constraints
- -1000 <= a, b <= 1000
How to think about it
Updated 2026-09-09Binary addition separates cleanly into two distinct mechanisms: adding bits while ignoring overflow, and detecting where both bits were one to generate carries. Bitwise XOR executes the half-adder sum without carry, while bitwise AND shifted left by one determines the exact carry positions. Repeating the merge until no carries exist computes the total.
Approaches, worst first
Iterative bit adder simulation
time O(1) · space O(1)
Simulate a hardware adder bit by bit from position zero to thirty-one with an explicit carry flag variable. Emulates the physical circuit correctly, but involves manual loop indexing across every bit.
Parallel XOR and carry propagationWrite this one
time O(1) · space O(1)
While carry b is non-zero, compute the carry as (a & b) << 1 and the sum as a ^ b in parallel. Replace a with the sum and b with the carry. Carries shift left and extinguish in at most thirty-two iterations.
Where people lose marks · 3
- Overwriting variable `a` with `a ^ b` before calculating the carry `(a & b) << 1` destroys the original bits of a needed for the carry mask.
- In languages like Python where integers have arbitrary precision, negative carries never overflow and propagate indefinitely without explicit 32-bit truncation masking using `0xFFFFFFFF`.
- Failing to cast the final result back to a signed 32-bit integer when working with bitwise operators that treat values as unsigned words.
The theory behind it
Bit Manipulation — the ground this problem stands on. All Bit Manipulation problems
What Bit Manipulation is
Bit manipulation is the practice of working directly on the individual ones and zeros that form numbers in computer memory. Every integer is stored as a tiny row of electrical switches that are either on or off. Instead of running arithmetic loops, bitwise operations flip, mask, shift, or combine these switches in a single hardware cycle. This allows compact storage of sets and blazing-fast checks without allocating extra memory.
When to reach for it
Reach for bit manipulation when problems ask to find a unique non-duplicate number, count set bits, determine if a value is a power of two, or pack a set of small booleans into a single integer. Prompts mentioning constant O(1) auxiliary space constraints on array queries often hint at XOR cancellation. It is also the foundation of bitmask dynamic programming, where subsets of up to twenty items are tracked as integer masks.
How the pattern works
Think of an integer as a fixed-length set of flags. Use bitwise AND to inspect if a specific bit is set, bitwise OR to turn a bit on, and bitwise XOR to flip a bit or cancel out matched pairs. Learn the standard bit tricks: n AND with n minus one clears the lowest set bit, which counts ones quickly, while n AND with negative n isolates the lowest set bit. When packing sets into masks, represent the empty set as zero and add item i by shifting one left by i and combining with OR.
What each operation costs
| Operation | Time |
|---|---|
| bitwise operation like AND, OR, or XOR | O(1) |
| count set bits across fixed integer width | O(1) |
| find single non-duplicate number using XOR | O(n) |
What usually goes wrong with Bit Manipulation
- Forgetting that bitwise operators have lower operator precedence than equality and arithmetic comparisons in most languages, evaluating expressions in the wrong order without parentheses.
- Using signed right shift instead of unsigned logical right shift when processing negative numbers, which fills high-order bits with ones instead of zeros.
- Shifting bits by thirty-two or more on standard 32-bit integers, causing undefined behavior or wrapped bit shifts that yield incorrect masks.
Which roles need this problem
Bit Manipulation is a core topic for these 9 roles — if you're targeting one of them, this problem is early in your path, not optional.
Secondary for 2 more roles, including ML Engineer, Information Retrieval Engineer.
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