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

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

O(n)

Understanding Time Complexity

Bit manipulation operations are basic steps computers use to handle numbers at the smallest level.

We want to know how the time to do these operations changes as the number size grows.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

int a = 5;          // 0101 in binary
int b = 9;          // 1001 in binary
int andResult = a & b;   // AND operation
int orResult = a | b;    // OR operation
int xorResult = a ^ b;   // XOR operation
int notResult = ~a;      // NOT operation
int leftShift = a << 2;  // Left shift by 2 bits
int rightShift = b >> 1; // Right shift by 1 bit
    

This code performs basic bit operations on two integers.

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: Each operation touches every bit once.

How Execution Grows With Input

As the number size grows (more bits), the operations take a bit longer because they process each bit.

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

Pattern observation: The time grows linearly with the number of bits.

Final Time Complexity

Time Complexity: O(n)

This means the time to do bit operations grows linearly with the number of bits in the number.

Common Mistake

[X] Wrong: "Bit operations always take constant time no matter the number size."

[OK] Correct: Actually, the time depends on how many bits the number has, so bigger numbers take more steps.

Interview Connect

Understanding bit operations and their time helps you write fast code and answer questions about low-level data handling.

Self-Check

"What if we used 128-bit numbers instead of 32-bit? How would the time complexity change?"

Practice

1. What does the bitwise AND operator (&) do when applied to two bits?

easy

A. Flips the bits from 0 to 1 and 1 to 0

B. Returns 1 if at least one bit is 1

C. Returns 1 only if both bits are 1

D. Returns 0 only if both bits are 0

Solution

1. Step 1: Understand bitwise AND operation

   The AND operator compares each bit of two numbers and returns 1 only if both bits are 1.

2. Step 2: Apply to example bits

   For bits 1 & 1, result is 1; for 1 & 0 or 0 & 1 or 0 & 0, result is 0.

3. Final Answer:

   Returns 1 only if both bits are 1 -> Option C

4. Quick Check:

   AND = 1 only if both bits 1 [OK]

Hint: AND returns 1 only when both bits are 1 [OK]

Common Mistakes:

• Confusing AND with OR operator
• Thinking AND flips bits
• Assuming AND returns 1 if any bit is 1

2. Which of the following is the correct syntax for left shifting an integer variable x by 3 positions in Java?

easy

A. x << 3;

B. x >> 3;

C. x <<< 3;

D. x >>> 3;

Solution

1. Step 1: Recall left shift operator syntax in Java

   Left shift operator is << and shifts bits to the left.

2. Step 2: Identify correct usage

   To shift variable x left by 3 bits, use x << 3;. Other options are right shifts or invalid.

3. Final Answer:

   x << 3; -> Option A

4. Quick Check:

   Left shift = x << number [OK]

Hint: Use << for left shift, >> for right shift [OK]

Common Mistakes:

• Using >>> for left shift (it's unsigned right shift)
• Using <<< which is invalid syntax
• Confusing left and right shift operators

3. What is the output of the following Java code?

int a = 5;  // binary 0101
int b = 3;  // binary 0011
int c = a ^ b;
System.out.println(c);

medium

A. 8

B. 7

C. 2

D. 6

Solution

1. Step 1: Convert numbers to binary

   a = 5 is 0101, b = 3 is 0011 in binary.

2. Step 2: Apply XOR operation bitwise

   XOR returns 1 if bits differ, 0 if same.
   0101 XOR 0011 = 0110 (binary) which is 6 decimal.

3. Final Answer:

   6 -> Option D

4. Quick Check:

   5 ^ 3 = 6 [OK]

Hint: XOR sets bits where inputs differ [OK]

Common Mistakes:

• Confusing XOR with OR or AND
• Calculating XOR incorrectly bitwise
• Assuming XOR adds numbers

4. Identify the error in the following Java code snippet:

int x = 8;
int y = ~x << 2;
System.out.println(y);

medium

A. No error; the code runs and prints a valid integer

B. The shift operator << must be used before the NOT operator ~

C. The bitwise NOT operator (~) cannot be used on integers

D. The variable y should be declared as long instead of int

Solution

1. Step 1: Analyze bitwise NOT and shift usage

   The NOT operator (~) flips all bits of x. Then the result is shifted left by 2 bits.

2. Step 2: Check Java syntax and types

   Both ~ and << operators work on int type. The expression is valid and prints an integer.

3. Final Answer:

   No error; the code runs and prints a valid integer -> Option A

4. Quick Check:

   ~ and << valid on int [OK]

Hint: Bitwise NOT and shifts work fine on int in Java [OK]

Common Mistakes:

• Thinking ~ cannot be used on int
• Assuming operator order is wrong
• Believing int can't hold shifted values

5. Given an integer n, which expression correctly toggles (flips) the 4th bit (counting from 0) of n using bitwise operators in Java?

hard

A. n = n | (1 << 4);

B. n = n ^ (1 << 4);

C. n = n & ~(1 << 4);

D. n = ~n << 4;

Solution

1. Step 1: Understand toggling a bit

   Toggling means flipping the bit: 0 becomes 1, 1 becomes 0.

2. Step 2: Identify correct operator for toggling

   XOR (^) with 1 at the bit position flips that bit. So n ^ (1 << 4) toggles the 4th bit.

3. Final Answer:

   n = n ^ (1 << 4); -> Option B

4. Quick Check:

   Toggling bit uses XOR with mask [OK]

Hint: Use XOR with mask to toggle bits [OK]

Common Mistakes:

• Using OR to toggle (only sets bit)
• Using AND with negation to toggle (clears bit)
• Using NOT and shift incorrectly