Set Clear Toggle a Specific Bit in DSA Python - Execution Trace

Concept Flow - Set Clear Toggle a Specific Bit

Start with number n

↓

Choose bit position p

↓

Select operation: Set / Clear / Toggle

↓

Create mask = 1 << p

↓

If Set: n = n | mask

↓

If Clear: n = n & ~mask

↓

If Toggle: n = n ^ mask

↓

Result: n with bit p changed

↓

End

This flow shows how to change a specific bit in a number by creating a mask and applying bitwise operations to set, clear, or toggle that bit.

Execution Sample

DSA Python

n = 13  # binary 1101
p = 2
mask = 1 << p
n = n | mask
print(bin(n))

This code sets the bit at position 2 of number 13 (binary 1101), turning it on.

Execution Table

Step	Operation	Number (decimal)	Number (binary)	Mask (binary)	Bit Position	Pointer Changes	Visual State (binary)
1	Start with n	13	1101	-	-	-	1101
2	Choose bit position p	13	1101	-	2	-	1101
3	Create mask = 1 << p	13	1101	100	2	-	1101
4	Set bit: n = n | mask	13	1101	100	2	n updated	1101
5	Print result	13	1101	100	2	-	1101
6	End	13	1101	100	2	-	1101

💡 Bit at position 2 was already set; number remains 13 (binary 1101)

Variable Tracker

Variable	Start	After Step 3	After Step 4	Final
n	13 (1101)	13 (1101)	13 (1101)	13 (1101)
p	-	2	2	2
mask	-	4 (100)	4 (100)	4 (100)

Key Moments - 3 Insights

Why does the number not change after setting bit 2 in this example?

Because in execution_table row 4, the bit at position 2 was already 1 in the original number (1101), so OR with mask 100 keeps it the same.

What does the mask 1 << p represent?

As shown in execution_table row 3, mask shifts 1 left by p positions to create a binary number with only the target bit set, used to change that bit.

How do we clear or toggle a bit differently?

Instead of OR (|) for set, use AND with NOT (~) mask to clear, or XOR (^) with mask to toggle, as described in concept_flow.

Visual Quiz - 3 Questions

Look at execution_table row 3, what is the binary mask created for bit position 2?

A 0010

B 0100

C 1000

D 0001

💡 Hint

Check the 'Mask (binary)' column in row 3 of execution_table

At which step does the number n get updated with the new bit set?

A Step 2

B Step 3

C Step 4

D Step 5

💡 Hint

Look at the 'Operation' and 'Pointer Changes' columns in execution_table

If the bit at position 2 was 0 initially, what would be the visual state after setting it?

A 1111

B 1001

C 1101

D 0101

💡 Hint

Setting bit 2 means turning that bit to 1; check how OR operation affects bits in execution_table

Concept Snapshot

Set, Clear, Toggle a bit:
- Create mask: 1 << position
- Set bit: n = n | mask
- Clear bit: n = n & ~mask
- Toggle bit: n = n ^ mask
- Bit positions start at 0 from right (LSB)

Full Transcript

This lesson shows how to change a specific bit in a number using bitwise operations. We start with a number n and a bit position p. We create a mask by shifting 1 left by p positions. To set the bit, we OR n with the mask. To clear, we AND n with the negation of the mask. To toggle, we XOR n with the mask. The example sets bit 2 of 13 (binary 1101). Since bit 2 was already set, the number stays the same. This method lets us control individual bits easily.

Practice

1. What does the operation num | (1 << k) do to the number num in terms of its bits?

easy

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

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

C. Toggles the k-th bit of num

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

Solution

1. Step 1: Understand bitwise OR with shifted 1

   The expression 1 << k creates a number with only the k-th bit set to 1.

2. Step 2: Apply OR operation to set 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 A

4. Quick Check:

   OR with 1 at bit k sets that bit [OK]

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

Common Mistakes:

• Confusing OR with AND operation
• Thinking it clears or toggles the bit
• Misunderstanding bit positions starting at 0

2. Which of the following Python expressions correctly clears (sets to 0) the k-th bit of an integer num?

easy

A. num & (1 << k)

B. num ^ (1 << k)

C. num | ~(1 << k)

D. num & ~(1 << k)

Solution

1. Step 1: Understand clearing a bit

   To clear the k-th bit, we want to keep all bits except the k-th bit set to 0.

2. Step 2: Use AND with NOT mask

   The mask ~(1 << k) has all bits set to 1 except the k-th bit which is 0. ANDing with this clears the k-th bit.

3. Final Answer:

   num & ~(1 << k) -> Option D

4. Quick Check:

   AND with inverted mask clears bit [OK]

Hint: AND with NOT of shifted 1 clears bit [OK]

Common Mistakes:

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

3. What is the output of the following code?

num = 42  # binary 101010
k = 1
result = num ^ (1 << k)
print(result)

medium

A. 40

B. 43

C. 44

D. 41

Solution

1. Step 1: Convert num and identify bit

   42 in binary is 101010. The bit positions (0-based) from right are: bit 0=0, bit 1=1, bit 2=0, bit 3=1, bit 4=0, bit 5=1.

2. Step 2: Toggle bit 1 using XOR

   1 << 1 is 2 (binary 10). XOR toggles bit 1: original bit 1 is 1, toggled to 0. So binary becomes 101000 which is 40 decimal.

3. Final Answer:

   40 -> Option A

4. Quick Check:

   XOR toggles bit 1 from 1 to 0 [OK]

Hint: XOR toggles bit; check original bit to find result [OK]

Common Mistakes:

• Confusing XOR with OR or AND
• Miscounting bit positions
• Forgetting bits are zero-indexed from right

4. The following code is intended to clear the 3rd bit (0-based) of num. What is the error?

num = 29  # binary 11101
k = 3
num = num | ~(1 << k)
print(num)

medium

A. Incorrect bit shift direction

B. Using OR instead of AND to clear the bit

C. Missing parentheses around bitwise NOT

D. No error, code works correctly

Solution

1. Step 1: Understand clearing bit logic

   To clear a bit, we must AND with the inverse mask, not OR.

2. Step 2: Identify incorrect operator usage

   The code uses OR (|) which sets bits, so it cannot clear the bit. It should use AND (&).

3. Final Answer:

   Using OR instead of AND to clear the bit -> Option B

4. Quick Check:

   Clear bit requires AND with NOT mask [OK]

Hint: Clear bit uses AND with NOT mask, not OR [OK]

Common Mistakes:

• Using OR instead of AND to clear bits
• Confusing bitwise NOT precedence
• Assuming code works without testing

5. You have a number num = 0. You want to toggle bits 0, 2, and 4 in sequence using the expression num = num ^ (1 << k). What is the final decimal value of num after toggling these bits?

hard

A. 15

B. 31

C. 21

D. 10

Solution

1. Step 1: Toggle bit 0 on num=0

   num = 0 ^ (1 << 0) = 0 ^ 1 = 1 (binary 00001)

2. Step 2: Toggle bit 2 on num=1

   num = 1 ^ (1 << 2) = 1 ^ 4 = 5 (binary 00101)

3. Step 3: Toggle bit 4 on num=5

   num = 5 ^ (1 << 4) = 5 ^ 16 = 21 (binary 10101)

4. Final Answer:

   21 -> Option C

5. Quick Check:

   Toggling bits 0,2,4 sets bits to 1, sum 1+4+16=21 [OK]

Hint: Toggle bits one by one with XOR, sum powers of two [OK]

Common Mistakes:

• Toggling bits in wrong order
• Miscounting bit positions
• Adding instead of XORing bits