Commonly Asked Data Structure Interview Questions on Bit Manipulation

Last Updated : 04 Mar, 2025

Bit manipulation is a powerful technique often used in technical interviews to optimize space and time complexities by directly working with the binary representations of numbers. It allows you to perform operations such as setting, clearing, or toggling individual bits, and efficiently checking conditions like even or odd numbers, divisibility, or power of two.

Questions on bit manipulation typically test your understanding of binary operations, shifts, and logical bitwise operations like AND, OR, XOR, and NOT. Mastering bit manipulation can significantly improve your problem-solving skills, especially when dealing with low-level operations, memory optimization, and algorithm efficiency.

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Theoretical Questions for Interviews on Bit Manipulation

1. What is the purpose of the bitwise AND operator?

The AND operator (&) returns 1 when both bits are 1; otherwise, it returns 0. It’s often used to check if a number is even or odd by performing n & 1.

2. How can you check if a number is a power of two using bit manipulation?

A number is a power of two if n & (n - 1) equals 0, and n > 0. This works because powers of two have only one bit set to 1.

3. What does the XOR operator do and how is it useful?

XOR (^) returns 1 when the bits are different. It’s used to find the difference between two numbers, or to toggle bits, such as swapping two numbers without a temporary variable.

4. How can you count the number of 1's (set bits) in a number?

You can use n & (n - 1) to repeatedly remove the rightmost set bit, and count the iterations. This is a common trick to count set bits efficiently.

5. What is the significance of the bitwise OR operator?

The OR operator (|) returns 1 if at least one bit is 1. It's used to set specific bits in a number.

6. How do you toggle a specific bit in a number?

To toggle a bit, use XOR with a mask. For example, n ^= (1 << k) will toggle the k-th bit of n.

7. What is the result of shifting a number to the left or right?

Left shifting (<<) multiplies a number by powers of two, while right shifting (>>) divides it by powers of two, with the right shift for signed numbers preserving the sign.

8. What is the bitwise NOT operator and what does it do?

The NOT operator (~) inverts all the bits of a number. It’s useful for flipping bits or calculating the complement of a number.

9. How would you swap two numbers using bitwise XOR?

You can swap two numbers without a temporary variable by doing

a = a ^ b
b = a ^ b
a = a ^ b

10. How can you check if a number is even or odd using bit manipulation?

To check if a number is odd, simply do n & 1. If the result is 1, the number is odd; if it’s 0, it’s even.

11. How can you check if two numbers have opposite signs using bit manipulation?

Two numbers have opposite signs if the sign bit differs. Check using the expression (a ^ b) < 0; this will be true if a and b have different signs.

12. How can you determine if a number is divisible by 3 using bit manipulation?

A number is divisible by 3 if the difference between the count of set bits at odd and even positions is a multiple of 3. This can be done efficiently with bit shifts and XOR operations.