Why Set Clear Toggle a Specific Bit in DSA Typescript?

The Big Idea

What if you could flip a single switch in a huge control panel instantly and perfectly every time?

The Scenario

Imagine you have a long list of light switches, each representing a feature in a game or a setting in an app. You want to turn one specific switch on, off, or flip it 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, causing bugs or wrong settings.

The Solution

Using bit operations lets you quickly and safely change just the switch you want by working with numbers. You can turn on, turn off, or flip a specific bit without affecting the rest.

Before vs After

✗ Before

let flags = 0b1010;
// To turn on bit 1 manually
flags = flags | (1 << 1);

✓ After

function setBit(flags: number, position: number): number {
  return flags | (1 << position);
}

What It Enables

This lets you control many on/off settings efficiently using just numbers, saving memory and speeding up your program.

Real Life Example

In a video game, you can store which power-ups a player has using bits. Turning a bit on means the player got that power-up, turning it off means they lost it, and toggling flips the state.

Key Takeaways

Manual changes to individual bits are slow and error-prone.

Bit operations let you change one bit without affecting others.

This technique is fast, memory-efficient, and widely used in programming.

Practice

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

easy

A. Toggles the bit at position pos

B. Clears the bit at position pos to 0

C. Checks if the bit at position pos is 1

D. Sets the bit at position pos to 1

Solution

1. Step 1: Understand bitwise OR with shifted 1

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

2. Step 2: Apply OR operation to set bit

   Using num | (1 << pos) sets the bit at pos to 1 without changing other bits.

3. Final Answer:

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

4. Quick Check:

   Bitwise OR with 1 at pos sets bit [OK]

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

Common Mistakes:

• Confusing set with clear operation
• Using AND instead of OR to set bit
• Thinking it toggles the bit

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

easy

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

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

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

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

Solution

1. Step 1: Understand clearing a bit

   To clear a bit, we AND the number with a mask that has 0 at the target bit and 1s elsewhere.

2. Step 2: Create mask with NOT operator

   ~(1 << pos) creates a mask with 0 at pos and 1s elsewhere, so num & ~(1 << pos) clears the bit.

3. Final Answer:

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

4. Quick Check:

   AND with NOT mask clears bit [OK]

Hint: Use AND with NOT shifted 1 to clear bit [OK]

Common Mistakes:

• Using OR instead of AND to clear bit
• Forgetting to negate the mask
• Using XOR which toggles instead of clears

3. What is the output of the following TypeScript code?

let num = 10; // binary 1010
let pos = 1;
num = num ^ (1 << pos);
console.log(num);

medium

A. 8

B. 10

C. 12

D. 14

Solution

1. Step 1: Understand initial values and bit positions

   Number 10 in binary is 1010. Bit positions (0-based) from right: pos 0=0, pos 1=1, pos 2=0, pos 3=1.

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

   1 << 1 is 2 (binary 0010). XOR toggles bit 1: 1010 ^ 0010 = 1000 (binary), which is 8 decimal.

3. Final Answer:

   8 -> Option A

4. Quick Check:

   Toggle bit 1 in 10 gives 8 [OK]

Hint: XOR toggles bit; toggle 1 in 1010 gives 1000 (8) [OK]

Common Mistakes:

• Confusing XOR with OR or AND
• Miscounting bit positions
• Assuming toggle sets bit always to 1

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

let num = 5; // binary 0101
let pos = 2;
num = num & (1 << pos);
console.log(num);

medium

A. It only keeps the bit at pos and clears others

B. It clears the bit instead of toggling

C. It sets the bit instead of toggling

D. It causes a syntax error

Solution

1. Step 1: Analyze the operation used

   The code uses num & (1 << pos), which ANDs num with a mask having 1 only at pos.

2. Step 2: Understand effect of AND with mask

   This operation keeps only the bit at pos and clears all other bits, not toggling the bit.

3. Final Answer:

   It only keeps the bit at pos and clears others -> Option A

4. Quick Check:

   AND with mask keeps only that bit [OK]

Hint: AND with mask keeps only that bit, doesn't toggle [OK]

Common Mistakes:

• Confusing AND with XOR for toggling
• Expecting toggle but using AND
• Ignoring effect on other bits

5. You have a number num = 29 (binary 11101). You want to toggle the bits at positions 0, 2, and 4 simultaneously. Which TypeScript code correctly does this?

hard

A. num = num | ((1 << 0) & (1 << 2) & (1 << 4));

B. num = num & ~((1 << 0) | (1 << 2) | (1 << 4));

C. num = num ^ ((1 << 0) | (1 << 2) | (1 << 4));

D. num = num ^ (1 << 0) & (1 << 2) & (1 << 4);

Solution

1. Step 1: Create mask for bits 0, 2, and 4

   Using OR to combine shifted bits: (1 << 0) | (1 << 2) | (1 << 4) creates mask 10101 binary (decimal 21).

2. Step 2: Use XOR to toggle bits

   XOR with this mask toggles bits 0, 2, and 4 in num.

3. Final Answer:

   num = num ^ ((1 << 0) | (1 << 2) | (1 << 4)); -> Option C

4. Quick Check:

   XOR with combined mask toggles multiple bits [OK]

Hint: Combine bits with OR, toggle with XOR [OK]

Common Mistakes:

• Using AND or OR instead of XOR to toggle
• Using AND between shifted bits instead of OR
• Not combining bits before toggling