Set Clear Toggle a Specific Bit in DSA Rust - 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 previous value.

beginner

How do you clear a specific bit in a number?

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

beginner

What does it mean to toggle a specific bit?

Toggling a bit means changing it from 0 to 1 or from 1 to 0 (flipping its value).

intermediate

In Rust, which operator is used to set a bit at position n?

Use the bitwise OR operator (|) with 1 shifted left by n: number | (1 << n).

intermediate

How do you clear a bit at position n in Rust?

Use bitwise AND with the negation of 1 shifted left by n: number & !(1 << n).

Which Rust expression sets the 3rd bit (0-based) of a number 'num'?

A num & (1 << 3)

B num | (1 << 3)

C num ^ (1 << 3)

D num & !(1 << 3)

Setting a bit uses OR (|) with 1 shifted left by the bit position.

How do you clear the 2nd bit of 'num' in Rust?

A num | (1 << 2)

B num & (1 << 2)

C num & !(1 << 2)

D num ^ (1 << 2)

Clearing a bit uses AND (&) with the negation of 1 shifted left by the bit position.

What does the XOR (^) operator do when used with 1 << n on a number?

A Toggles the nth bit

B Clears the nth bit to 0

C Sets the nth bit to 1

D Leaves the number unchanged

XOR with 1 flips the bit: 0 becomes 1, 1 becomes 0.

If a number is 0b0101 and you toggle the 0th bit, what is the new number in binary?

A 0b0111

B 0b0101

C 0b0001

D 0b0100

Toggling the 0th bit flips it from 1 to 0, so 0b0101 becomes 0b0100.

Which operation would you use to check if the 4th bit of a number is set?

A number & (1 << 4)

B number | (1 << 4)

C number ^ (1 << 4)

D number & !(1 << 4)

AND with 1 shifted left by 4 isolates the 4th bit to check if it is 1.

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

Think about how each bitwise operator affects bits.

Describe a real-life example where toggling a bit might be useful.

Consider a light switch or a yes/no setting.

Practice

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

easy

A. Sets the bit at position pos to 1

B. Clears the bit at position pos to 0

C. Toggles the bit at position pos

D. Checks if the bit at position pos is set

Solution

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

   The expression 1 << pos creates a number with only the bit at position pos set to 1, all others 0.

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

   Using num | (1 << pos) sets the bit at pos to 1 regardless of its previous value, leaving other bits unchanged.

3. Final Answer:

   Sets the bit at position pos to 1 -> Option A

4. Quick Check:

   OR with 1 at pos sets bit to 1 [OK]

Hint: OR with 1 at position sets that bit to 1 [OK]

Common Mistakes:

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

2. Which of the following Rust code snippets correctly clears (sets to 0) the bit at position pos in num?

easy

A. num & (1 << pos)

B. num & !(1 << pos)

C. num | !(1 << pos)

D. num ^ (1 << pos)

Solution

1. Step 1: Create mask with 0 at pos and 1 elsewhere

   The expression !(1 << pos) creates a mask with all bits 1 except bit pos which is 0.

2. Step 2: AND operation clears bit at pos

   Using num & !(1 << pos) clears the bit at pos to 0, keeping other bits unchanged.

3. Final Answer:

   num & !(1 << pos) -> Option B

4. Quick Check:

   AND with inverted mask clears bit [OK]

Hint: AND with NOT mask clears bit at position [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 Rust code?

let mut num = 0b1010; // binary 10
let pos = 1;
num ^= 1 << pos;
println!("{:04b}", num);

medium

A. 1000

B. 1010

C. 1011

D. 1110

Solution

1. Step 1: Understand initial value and bit position

   Initial num is binary 1010 (decimal 10). Position pos is 1 (counting from 0 at right).

2. Step 2: Toggle bit at position 1 using XOR

   1 << pos is 0010. XOR toggles bit 1: 1010 XOR 0010 = 1000 (decimal 8).

3. Final Answer:

   1000 -> Option A

4. Quick Check:

   XOR toggles bit 1: 1010 -> 1000 [OK]

Hint: XOR with 1 toggles the bit at position [OK]

Common Mistakes:

• Confusing XOR with OR or AND
• Miscounting bit positions
• Printing decimal instead of binary

4. Identify the error in this Rust code that tries to toggle the bit at position pos in num:

let mut num = 0b1001;
let pos = 2;
num = num | (1 << pos);
num = num ^ (1 << pos);
println!("{:04b}", num);

medium

A. The code will cause a compile error

B. The bit position is out of range

C. The bit is toggled twice, so no change occurs

D. The OR operator should be AND to toggle

Solution

1. Step 1: Analyze the first operation (OR)

   num | (1 << pos) sets bit 2 to 1. Bit 2 was 0 in 1001, so num becomes 1101.

2. Step 2: Analyze the second operation (XOR)

   num ^ (1 << pos) toggles bit 2 from 1 back to 0, resulting in 1001.

3. Step 3: Check final output

   After both operations, bit 2 was set then toggled back, so no net change occurs.

4. Final Answer:

   The bit is toggled twice, so no change occurs -> Option C

5. Quick Check:

   Setting then toggling same bit cancels out [OK]

Hint: Setting then toggling same bit cancels effect [OK]

Common Mistakes:

• Assuming OR then XOR always toggles bit
• Ignoring bit position indexing
• Expecting compile error where none exists

5. Given a 8-bit number num = 0b11001100, write the result after toggling bits at positions 2, 3, and 7 in sequence using Rust bitwise operations. What is the final binary value?

hard

A. 10001100

B. 01001100

C. 11001100

D. 01000000

Solution

1. Step 1: Initial value and bit positions

   Initial num is 11001100 (bits 7 to 0). Positions to toggle: 2, 3, 7.

2. Step 2: Toggle bit 2

   Bit 2 is 1 (counting from 0 rightmost). Toggle flips it to 0: 11001100 -> 11001000.

3. Step 3: Toggle bit 3

   Bit 3 is 1. Toggle flips it to 0: 11001000 -> 11000000.

4. Step 4: Toggle bit 7

   Bit 7 is 1. Toggle flips it to 0: 11000000 -> 01000000.

5. Step 5: Final binary value

   Final value is 01000000 in binary (bits 7,3,2 toggled to 0, others unchanged).

6. Final Answer:

   01000000 -> Option D

7. Quick Check:

   Toggle bits 2,3,7 flips those bits [OK]

Hint: Toggle bits one by one with XOR [OK]

Common Mistakes:

• Miscounting bit positions from right
• Forgetting to toggle bits in sequence
• Confusing toggle with set or clear