Bit Manipulation Basics AND OR XOR NOT Left Right Shift in DSA Javascript - Time & Space Complexity

Time Complexity: Bit Manipulation Basics AND OR XOR NOT Left Right Shift

O(1)

Understanding Time Complexity

Bit manipulation uses simple operations on numbers at the bit level.

We want to know how fast these operations run as input size changes.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

const a = 5;       // 0101 in binary
const b = 3;       // 0011 in binary

const andResult = a & b;   // AND operation
const orResult = a | b;    // OR operation
const xorResult = a ^ b;   // XOR operation
const notResult = ~a;      // NOT operation
const leftShift = a << 1;  // Left shift by 1
const rightShift = a >> 1; // Right shift by 1
    

This code performs basic bit operations on two numbers.

Identify Repeating Operations

Each bit operation works on all bits of the number at once.

• Primary operation: Bitwise AND, OR, XOR, NOT, and shifts
• How many times: Once per operation, affecting all bits simultaneously

How Execution Grows With Input

Operations process each bit in the number, so time grows with the number of bits.

Input Size (bits)	Approx. Operations
8	8 operations
32	32 operations
64	64 operations

Pattern observation: Time grows linearly with the number of bits in the input.

Final Time Complexity

Time Complexity: O(1)

This means bit operations run in constant time because the number of bits is fixed by the system.

Common Mistake

[X] Wrong: "Bitwise operations take longer as numbers get bigger."

[OK] Correct: The number size is limited by fixed bits (like 32 or 64), so operations always take the same time.

Interview Connect

Knowing bit operations run fast helps you choose them for quick checks or toggles in coding problems.

Self-Check

"What if we used big integers with thousands of bits? How would the time complexity change?"

Practice

1. What is the result of the bitwise AND operation between 5 and 3? (5 & 3)

easy

A. 1

B. 7

C. 0

D. 8

Solution

1. Step 1: Convert numbers to binary

   5 in binary is 0101, 3 in binary is 0011.

2. Step 2: Perform bitwise AND

   0101 & 0011 = 0001 (only bits set in both numbers remain set).

3. Final Answer:

   1 -> Option A

4. Quick Check:

   5 & 3 = 1 [OK]

Hint: AND keeps bits set in both numbers only [OK]

Common Mistakes:

• Confusing AND with OR operation
• Not converting numbers to binary before operation
• Assuming decimal addition instead of bitwise

2. Which of the following is the correct syntax for performing a bitwise XOR operation between variables a and b in JavaScript?

easy

A. let result = a | b;

B. let result = a && b;

C. let result = a % b;

D. let result = a ^ b;

Solution

1. Step 1: Identify bitwise XOR operator in JavaScript

   The XOR operator is represented by the caret symbol (^).

2. Step 2: Check syntax correctness

   let result = a ^ b; uses a ^ b, which is the correct syntax for bitwise XOR.

3. Final Answer:

   let result = a ^ b; -> Option D

4. Quick Check:

   XOR operator is ^ in JavaScript [OK]

Hint: XOR uses ^ symbol in JavaScript [OK]

Common Mistakes:

• Using && which is logical AND, not bitwise
• Using | which is bitwise OR, not XOR
• Using % which is modulo, unrelated to bits

3. What will be the output of the following JavaScript code?

let x = 8; // binary 1000
let y = x >> 2;
console.log(y);

medium

A. 2

B. 4

C. 1

D. 0

Solution

1. Step 1: Understand right shift operation

   Right shift by 2 means move bits 2 places to the right, dropping the rightmost bits.

2. Step 2: Apply right shift on binary 1000

   1000 >> 2 becomes 0010, which is decimal 2.

3. Final Answer:

   2 -> Option A

4. Quick Check:

   8 >> 2 = 2 [OK]

Hint: Right shift divides by 2 for each shift [OK]

Common Mistakes:

• Confusing right shift with left shift
• Not converting binary to decimal after shift
• Assuming shift adds zeros on left without dropping bits

4. Find the error in the following code snippet that attempts to flip all bits of a number n using bitwise NOT:

let n = 5;
let flipped = ~n;
console.log(flipped);

What is the issue?

medium

A. Missing parentheses around ~n

B. Bitwise NOT returns a negative number due to two's complement representation

C. Variable n must be a string for bitwise NOT

D. Bitwise NOT operator (~) is not supported in JavaScript

Solution

1. Step 1: Understand bitwise NOT in JavaScript

   Bitwise NOT flips all bits and returns the two's complement negative number.

2. Step 2: Explain why output is negative

   For 5 (00000101), ~5 flips bits to 11111010 which is -6 in two's complement.

3. Final Answer:

   Bitwise NOT returns a negative number due to two's complement representation -> Option B

4. Quick Check:

   ~n flips bits and returns negative number [OK]

Hint: Bitwise NOT flips bits and returns negative in JS [OK]

Common Mistakes:

• Expecting positive flipped bits as output
• Thinking ~ is unsupported operator
• Assuming input must be string for bitwise ops

5. You want to set the 3rd bit (0-indexed from right) of a number num to 1 without changing other bits. Which expression correctly does this in JavaScript?

hard

A. num = num ^ (1 << 3);

B. num = num & (1 << 3);

C. num = num | (1 << 3);

D. num = num << 3;

Solution

1. Step 1: Understand setting a bit using OR and shift

   Left shift 1 by 3 gives 00001000, which targets the 3rd bit.

2. Step 2: Use OR to set the bit without changing others

   OR with this mask sets the 3rd bit to 1, keeping others unchanged.

3. Final Answer:

   num = num | (1 << 3); -> Option C

4. Quick Check:

   Use OR with shifted 1 to set bit [OK]

Hint: Use OR with (1 << bit_position) to set bit [OK]

Common Mistakes:

• Using AND which clears bits instead of setting
• Using XOR which toggles bits and may unset
• Using left shift alone which changes number value