Why Set Clear Toggle a Specific Bit in DSA Python?

The Big Idea

What if you could flip a single switch in a huge control panel with just one quick move?

The Scenario

Imagine you have a long list of light switches, each representing a feature in a software. You want to turn on, turn off, or flip just one switch without touching the others.

The Problem

Manually checking and changing each switch one by one is slow and easy to mess up. You might accidentally change the wrong switch or forget to update some.

The Solution

Using bit operations lets you directly target and change only the switch you want, quickly and safely, without affecting the others.

Before vs After

✗ Before

flags = 0b1010
# To turn on 3rd switch
flags = flags | 0b0100
# To turn off 2nd switch
flags = flags & 0b1101

✓ After

def set_bit(flags, position):
    return flags | (1 << position)

def clear_bit(flags, position):
    return flags & ~(1 << position)

def toggle_bit(flags, position):
    return flags ^ (1 << position)

What It Enables

This lets you control individual features or settings efficiently using just numbers.

Real Life Example

In video games, bit flags control which abilities a character has active without needing many separate variables.

Key Takeaways

Manual changes are slow and error-prone.

Bit operations target specific bits directly.

They make managing multiple on/off settings easy and fast.

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