Set Clear Toggle a Specific Bit in DSA C# - Execution Trace

Concept Flow - Set Clear Toggle a Specific Bit

Start with number

↓

Choose bit position

↓

Select operation: Set / Clear / Toggle

↓

Apply bitwise mask

↓

Update number with new bit value

↓

Resulting number with bit changed

This flow shows how to pick a bit position and apply set, clear, or toggle operation using bitwise masks to update the number.

Execution Sample

DSA C#

int num = 13; // binary 1101
int pos = 2;
// Set bit at pos
num = num | (1 << pos);
Console.WriteLine(num);

This code sets the bit at position 2 (0-based from right) in number 13.

Execution Table

Step	Operation	Bit Position	Mask (binary)	Number Before (binary)	Number After (binary)	Resulting Number
1	Start	-	-	1101	1101	13
2	Calculate mask	2	0100	1101	1101	13
3	Set bit (num | mask)	2	0100	1101	1101	13
4	Result	-	-	-	1101	13
5	Clear bit (num & ~mask)	2	0100	1101	1001	9
6	Toggle bit (num ^ mask)	2	0100	1101	1001	9
7	Toggle bit again (num ^ mask)	2	0100	1001	1101	13
8	End	-	-	-	-	-

💡 All operations done for bit position 2 on initial number 13.

Variable Tracker

Variable	Start	After Set	After Clear	After Toggle 1	After Toggle 2	Final
num (decimal)	13	13	9	9	13	13
num (binary)	1101	1101	1001	1001	1101	1101
pos	2	2	2	2	2	2
mask (binary)	0100	0100	0100	0100	0100	0100

Key Moments - 3 Insights

Why does setting a bit use OR (|) with the mask?

Because OR with 1 at the bit position ensures that bit becomes 1 without changing other bits, as shown in execution_table step 3.

Why do we clear a bit using AND (&) with the negated mask (~mask)?

AND with 0 at the bit position clears that bit to 0, while keeping others unchanged, as seen in step 5 of execution_table.

How does toggling a bit with XOR (^) work?

XOR flips the bit: if it was 1 it becomes 0, if 0 it becomes 1. This is shown in steps 6 and 7 where toggling twice returns to original.

Visual Quiz - 3 Questions

Look at the execution_table, what is the binary value of num after clearing bit 2?

A 1101

B 1001

C 0100

D 1111

💡 Hint

Check execution_table row 5 under 'Number After (binary)' column.

At which step does toggling bit 2 first change num from 1101 to 1001?

A Step 6

B Step 5

C Step 3

D Step 7

💡 Hint

Look at execution_table rows 6 and 7 for toggle operations.

If we change pos to 1, what would be the mask in binary?

A 0001

B 0100

C 0010

D 1000

💡 Hint

Mask is 1 shifted left by pos bits; see variable_tracker mask value for pos=2.

Concept Snapshot

Set, Clear, Toggle a bit at position pos in number num:
- Set: num = num | (1 << pos)
- Clear: num = num & ~(1 << pos)
- Toggle: num = num ^ (1 << pos)
Bit positions start at 0 from right (least significant bit).
Use bitwise masks to change only the target bit without affecting others.

Full Transcript

This lesson shows how to change a specific bit in a number using bitwise operations. We start with a number and pick a bit position. To set the bit, we use OR with a mask that has 1 at that position. To clear the bit, we use AND with the negation of that mask. To toggle, we use XOR with the mask. The execution table traces these steps on number 13 (binary 1101) at bit position 2. Variable tracker shows how num and mask change after each operation. Key moments clarify why each bitwise operation works. The quiz tests understanding of these changes and mask calculations.

Practice

1. What does the operation number |= (1 << position) do to the bit at position in number?

easy

A. Toggles the bit at position

B. Clears the bit at position to 0

C. Sets the bit at position to 1

D. Checks if the bit at position is set

Solution

1. Step 1: Understand the bitwise OR with shifted 1

   The expression 1 << position creates a number with only the bit at position set to 1. Using OR (|=) with this sets that bit in number to 1 without changing other bits.

2. Step 2: Effect on the bit at position

   Since OR with 1 always results in 1, the bit at position is set to 1 regardless of its previous value.

3. Final Answer:

   Sets the bit at position to 1 -> Option C

4. Quick Check:

   OR with 1 sets bit [OK]

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

Common Mistakes:

• Confusing OR with XOR for toggling
• Thinking it clears the bit
• Assuming it checks the bit instead

2. Which of the following C# statements correctly clears (sets to 0) the bit at position pos in an integer num?

easy

A. num &= ~(1 << pos);

B. num |= (1 << pos);

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

D. num = num << pos;

Solution

1. Step 1: Understand clearing a bit

   To clear a bit, we use AND with the complement of a mask that has 1 at the target bit. The mask is 1 << pos, so complement is ~(1 << pos).

2. Step 2: Apply AND with complemented mask

   Using num &= ~(1 << pos); clears the bit at pos while leaving others unchanged.

3. Final Answer:

   num &= ~(1 << pos); -> Option A

4. Quick Check:

   AND with complement clears bit [OK]

Hint: Use AND with NOT mask to clear a bit [OK]

Common Mistakes:

• Using OR instead of AND to clear
• Using XOR which toggles instead of clears
• Using left shift alone which changes number

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

int num = 10; // binary 1010
int pos = 1;
num ^= (1 << pos);
Console.WriteLine(num);

medium

A. 10

B. 14

C. 12

D. 8

Solution

1. Step 1: Understand initial number and bit position

   Number 10 in binary is 1010. Position 1 means the second bit from right (0-based). Bit at position 1 is 1.

2. Step 2: Apply XOR to toggle bit at position 1

   XOR toggles the bit. Since bit at position 1 is 1, toggling it changes it to 0. New binary is 1000 which is decimal 8.

3. Final Answer:

   8 -> Option D

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 XOR with OR or AND
• Miscounting bit positions (0-based)
• Assuming no change if bit is 1

4. The following code is intended to toggle the bit at position pos in num. What is the error?

int num = 5; // binary 0101
int pos = 2;
num = num & (1 << pos);
Console.WriteLine(num);

medium

A. It clears all bits except the one at pos

B. It toggles the bit correctly

C. It sets the bit at pos to 1

D. It causes a syntax error

Solution

1. Step 1: Analyze the operation used

   The code uses AND (&) with 1 << pos. This keeps only the bit at pos if it was set, clearing all others.

2. Step 2: Compare with toggle operation

   Toggling requires XOR (^), not AND. So this code does not toggle but masks all bits except the one at pos.

3. Final Answer:

   It clears all bits except the one at pos -> Option A

4. Quick Check:

   AND with mask keeps only that bit [OK]

Hint: Use XOR to toggle, AND masks bits [OK]

Common Mistakes:

• Using AND instead of XOR for toggle
• Expecting toggle but getting masked value
• Confusing bitwise operators

5. You have an integer num and want to toggle the bit at position pos only if it is currently set (1). Which code snippet correctly does this?

hard

A. if ((num ^ (1 << pos)) != 0) num ^= (1 << pos);

B. if ((num & (1 << pos)) != 0) num ^= (1 << pos);

C. if ((num & ~(1 << pos)) != 0) num ^= (1 << pos);

D. if ((num | (1 << pos)) != 0) num ^= (1 << pos);

Solution

1. Step 1: Check if bit at pos is set

   Using num & (1 << pos) checks if bit at pos is 1. If result is not zero, bit is set.

2. Step 2: Toggle bit only if set

   If bit is set, toggle it using XOR: num ^= (1 << pos);. This flips the bit from 1 to 0.

3. Final Answer:

   if ((num & (1 << pos)) != 0) num ^= (1 << pos); -> Option B

4. Quick Check:

   Check bit with AND, toggle with XOR [OK]

Hint: Check bit with AND before toggling with XOR [OK]

Common Mistakes:

• Using OR instead of AND to check bit
• Toggling without checking bit first
• Using incorrect mask complement