Set Clear Toggle a Specific Bit in DSA Python - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does it mean to set a specific bit in a number?

Setting a bit means changing that bit to 1, regardless of its current value.

beginner

How do you clear a specific bit in a number?

Clearing a bit means changing that bit to 0, regardless of its current value.

beginner

What does toggle a bit mean?

Toggling a bit means changing it from 0 to 1 or from 1 to 0.

beginner

Which operator is used to set a bit at position pos in Python?

Use the bitwise OR operator (|) with (1 << pos). Example: num | (1 << pos)

beginner

How do you clear a bit at position pos using bitwise operators?

Use bitwise AND (&) with the negation of (1 << pos): num & ~(1 << pos)

What is the result of setting bit 2 (0-based) in the number 8 (binary 1000)?

A 12 (binary 1100)

B 10 (binary 1010)

C 14 (binary 1110)

D 8 (binary 1000)

Setting bit 2 means turning the third bit from right to 1. 8 is 1000, setting bit 2 adds 4 (0100), so 1000 | 0100 = 1100 (12).

Which operation toggles a bit at position pos?

A num | (1 << pos)

B num & ~(1 << pos)

C num << pos

D num ^ (1 << pos)

XOR (^) with (1 << pos) flips the bit at pos: 0 becomes 1, 1 becomes 0.

Clearing a bit means:

A Flipping its value

B Setting it to 1

C Setting it to 0

D Leaving it unchanged

Clearing a bit means making that bit 0.

What does the expression num & ~(1 << pos) do?

A Sets bit pos to 1

B Clears bit pos to 0

C Toggles bit pos

D Checks if bit pos is set

It clears the bit at position pos by ANDing with the inverse mask.

If num = 5 (binary 0101), what is the result of toggling bit 0?

A 4 (binary 0100)

B 7 (binary 0111)

C 1 (binary 0001)

D 5 (binary 0101)

Toggling bit 0 flips the rightmost bit: 0101 ^ 0001 = 0100 (4).

Explain how to set, clear, and toggle a specific bit in a number using bitwise operators.

Think about how each operator affects bits at a given position.

Describe a real-life example where setting, clearing, or toggling bits might be useful.

Think about simple yes/no settings stored in one number.

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