Set Clear Toggle a Specific Bit in DSA C

Mental Model

We change one specific bit in a number to 1, 0, or flip it without affecting other bits.

Analogy: Imagine a row of light switches where each switch controls one light. Setting a bit is like turning a specific switch on, clearing is turning it off, and toggling is flipping its current state.

Number bits: 0 0 1 0 1 1 0 1
Positions:  7 6 5 4 3 2 1 0
Toggle bit 3:
Before:     0 0 1 0 1 1 0 1
After:      0 0 1 0 0 1 0 1

Dry Run Walkthrough

Input: number = 45 (binary 00101101), bit position = 3

Goal: Set bit 3 to 1, clear bit 3 to 0, and toggle bit 3

Step 1: Set bit 3 to 1 using OR with mask 1 << 3

00101101 (45) OR 00001000 (8) = 00101101 (45)

Why: Bit 3 is already 1, so setting it keeps the number same

Step 2: Clear bit 3 to 0 using AND with NOT mask ~(1 << 3)

00101101 (45) AND 11110111 (247) = 00100101 (37)

Why: Clearing bit 3 changes it from 1 to 0

Step 3: Toggle bit 3 using XOR with mask 1 << 3

00100101 (37) XOR 00001000 (8) = 00101101 (45)

Why: Toggling flips bit 3 back to 1

Result:

Final values: Set bit 3: 45 (00101101)
Clear bit 3: 37 (00100101)
Toggle bit 3: 45 (00101101)

Annotated Code

DSA C

#include <stdio.h>

// Set bit at position pos to 1
unsigned int setBit(unsigned int num, int pos) {
    return num | (1U << pos); // OR sets bit at pos
}

// Clear bit at position pos to 0
unsigned int clearBit(unsigned int num, int pos) {
    return num & ~(1U << pos); // AND with NOT clears bit at pos
}

// Toggle bit at position pos
unsigned int toggleBit(unsigned int num, int pos) {
    return num ^ (1U << pos); // XOR flips bit at pos
}

int main() {
    unsigned int number = 45; // 00101101
    int position = 3;

    unsigned int set_result = setBit(number, position);
    unsigned int clear_result = clearBit(number, position);
    unsigned int toggle_result = toggleBit(clear_result, position);

    printf("Set bit %d: %u (binary 00101101)\n", position, set_result);
    printf("Clear bit %d: %u (binary 00100101)\n", position, clear_result);
    printf("Toggle bit %d: %u (binary 00101101)\n", position, toggle_result);

    return 0;
}

return num | (1U << pos);

Set bit at position pos by OR with mask

return num & ~(1U << pos);

Clear bit at position pos by AND with inverted mask

return num ^ (1U << pos);

Toggle bit at position pos by XOR with mask

Output

Set bit 3: 45 (binary 00101101)

Clear bit 3: 37 (binary 00100101)

Toggle bit 3: 45 (binary 00101101)

Complexity Analysis

Time: O(1) because bitwise operations take constant time regardless of input size

Space: O(1) because no extra memory is used beyond variables

vs Alternative: Using bitwise operations is much faster and simpler than converting to binary strings and manipulating characters

Edge Cases

bit position is 0 (least significant bit)

Operations correctly affect the rightmost bit

DSA C

return num | (1U << pos);

bit position is maximum for unsigned int (e.g., 31)

Operations correctly affect the highest bit without overflow

DSA C

return num & ~(1U << pos);

number is 0

Setting bit sets that bit to 1, clearing keeps 0, toggling flips bit

DSA C

return num ^ (1U << pos);

When to Use This Pattern

When you need to change a single bit in a number without affecting others, use bitwise set, clear, or toggle operations because they are fast and direct.

Common Mistakes

Mistake: Using left shift without unsigned suffix causing undefined behavior
Fix: Use 1U to ensure shifting unsigned integer

Mistake: Clearing bit using OR instead of AND with NOT mask
Fix: Use AND with inverted mask to clear bit

Mistake: Toggling bit using OR or AND instead of XOR
Fix: Use XOR to flip the bit

Summary

It changes one specific bit in a number to 1, 0, or flips it.

Use it when you want to manipulate individual bits efficiently.

The key is using bitwise OR to set, AND with NOT to clear, and XOR to toggle bits.

Practice

1. What does the operation num |= (1 << k) do to the integer num?

easy

A. Toggles the k-th bit of num

B. Clears the k-th bit of num to 0

C. Checks if the k-th bit of num is set

D. Sets the k-th bit of num to 1

Solution

1. Step 1: Understand the bit shift operation

   1 << k creates a number with only the k-th bit set to 1 and others 0.

2. Step 2: Apply bitwise OR to set the bit

   Using num |= (1 << k) sets the k-th bit of num to 1 without changing other bits.

3. Final Answer:

   Sets the k-th bit of num to 1 -> Option D

4. Quick Check:

   Set bit = OR with 1 shifted [OK]

Hint: Use OR with 1 shifted to set a bit [OK]

Common Mistakes:

• Confusing set with clear operation
• Using AND instead of OR to set bits
• Misunderstanding bit positions starting from 0

2. Which of the following C statements correctly clears the k-th bit of an integer num?

easy

A. num = num << k;

B. num &= ~(1 << k);

C. num ^= (1 << k);

D. num |= (1 << k);

Solution

1. Step 1: Understand clearing a bit

   Clearing means setting the bit to 0. We use AND with the complement of the bit mask.

2. Step 2: Analyze the options

   num &= ~(1 << k); clears the k-th bit by ANDing with all 1s except 0 at k-th bit.

3. Final Answer:

   num &= ~(1 << k); -> Option B

4. Quick Check:

   Clear bit = AND with NOT of shifted 1 [OK]

Hint: Use AND with NOT of shifted 1 to clear bit [OK]

Common Mistakes:

• Using OR instead of AND to clear bits
• Forgetting to negate the mask
• Using XOR which toggles instead of clears

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

int num = 10; // binary 1010
int k = 1;
num ^= (1 << k);
printf("%d", num);

medium

A. 12

B. 10

C. 8

D. 14

Solution

1. Step 1: Understand initial value and bit positions

   num = 10 (binary 1010), k = 1 means second bit from right (0-based).

2. Step 2: Apply XOR to toggle the k-th bit

   Toggle bit 1: bit at position 1 is 1 in 1010, toggling it changes to 0, so binary becomes 1000 which is 8.

3. Final Answer:

   8 -> Option C

4. Quick Check:

   Toggle bit 1 in 1010 = 1000 = 8 [OK]

Hint: XOR toggles bit: 1 becomes 0, 0 becomes 1 [OK]

Common Mistakes:

• Confusing toggle with set or clear
• Miscounting bit positions starting from 1 instead of 0
• Assuming XOR always sets bit

4. The following code is intended to clear the 3rd bit of num. What is the error?

int num = 15; // binary 1111
int k = 3;
num = num & (1 << k);

medium

A. It clears all bits except the 3rd bit

B. It sets the 3rd bit instead of clearing

C. It toggles the 3rd bit instead of clearing

D. No error, code works correctly

Solution

1. Step 1: Analyze the bitwise AND operation

   The code does num & (1 << k), which keeps only the k-th bit and clears others.

2. Step 2: Understand the intended operation

   To clear the k-th bit, we must AND with the complement of the bit mask, not the mask itself.

3. Final Answer:

   It clears all bits except the 3rd bit -> Option A

4. Quick Check:

   AND with mask keeps only that bit, not clears it [OK]

Hint: Clear bit = AND with NOT of mask, not mask alone [OK]

Common Mistakes:

• Using mask instead of its complement to clear bit
• Confusing AND with OR for clearing bits
• Assuming AND with mask clears bit

5. You want to toggle the 0th and 2nd bits of an integer num simultaneously. Which expression correctly does this in C?

hard

A. num ^= (1 << 0) | (1 << 2);

B. num |= (1 << 0) & (1 << 2);

C. num &= ~( (1 << 0) | (1 << 2) );

D. num = (num << 0) ^ (num << 2);

Solution

1. Step 1: Understand toggling multiple bits

   Toggling bits uses XOR. To toggle multiple bits, XOR with mask having those bits set.

2. Step 2: Create mask for bits 0 and 2

   Mask is (1 << 0) | (1 << 2), which sets bits 0 and 2 to 1.

3. Step 3: Apply XOR with mask

   Expression num ^= (1 << 0) | (1 << 2); toggles both bits simultaneously.

4. Final Answer:

   num ^= (1 << 0) | (1 << 2); -> Option A

5. Quick Check:

   XOR with combined mask toggles multiple bits [OK]

Hint: XOR with ORed shifted bits toggles multiple bits [OK]

Common Mistakes:

• Using AND or OR instead of XOR for toggling
• Incorrectly combining masks with AND
• Misusing shift operations in toggle