Why Bit Manipulation and When It Beats Arithmetic in DSA Typescript - Test Your Knowledge

Practice - 5 Tasks

1fill in blank

easy

Complete the code to perform a left bit shift by 1, which doubles the number.

DSA Typescript

const doubled = num [1] 1;

Drag options to blanks, or click blank then click option'

A<<

B>>

C+

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using right shift (>>) instead of left shift.

Using addition (+) instead of bit shift.

Using the left shift operator (<<) by 1 moves all bits one place to the left, effectively multiplying the number by 2.

2fill in blank

medium

Complete the code to check if the least significant bit of a number is 1 (odd number check).

DSA Typescript

const isOdd = (num & [1]) === 1;

Drag options to blanks, or click blank then click option'

A2

B3

C0

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Using 2 instead of 1 for the mask.

Checking equality with 0 instead of 1.

Using bitwise AND with 1 checks the least significant bit. If it is 1, the number is odd.

3fill in blank

hard

Fix the error in the code to toggle the 3rd bit (bit index 2) of a number.

DSA Typescript

const toggled = num [1] (1 << 2);

Drag options to blanks, or click blank then click option'

A&

B|

C^

D>>

Attempts:

3 left

💡 Hint

Common Mistakes

Using AND (&) which clears bits.

Using OR (|) which sets bits but does not toggle.

The XOR operator (^) toggles bits. Using it with (1 << 2) flips the 3rd bit.

4fill in blank

hard

Fill both blanks to create a mask that clears the 3rd bit (bit index 2) of a number.

DSA Typescript

const mask = ~(1 [1] [2]);

Drag options to blanks, or click blank then click option'

A<<

B1

C2

D&

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong shift amount.

Not inverting the mask.

Shift 1 left by 2 to get a mask for the 3rd bit, then invert it to clear that bit.

5fill in blank

hard

Fill all three blanks to create a function that sets the nth bit of a number.

DSA Typescript

function setBit(num: number, n: number): number {
  return num [1] ([2] [3] n);
}

Drag options to blanks, or click blank then click option'

A|

B1

C<<

D&

Attempts:

3 left

💡 Hint

Common Mistakes

Using AND instead of OR.

Shifting num instead of 1.

Use OR (|) with 1 shifted left by n to set the nth bit of num.

Practice

1. Why is bit manipulation often faster than arithmetic operations like multiplication or division?

easy

A. Because bit manipulation works directly on binary digits using CPU instructions

B. Because arithmetic operations use more memory than bit manipulation

C. Because bit manipulation requires more complex algorithms

D. Because arithmetic operations are not supported by modern CPUs

Solution

1. Step 1: Understand how bit manipulation works

   Bit manipulation uses CPU instructions that directly change bits, which are the smallest data units.

2. Step 2: Compare with arithmetic operations

   Arithmetic like multiplication or division involves multiple CPU cycles and more complex calculations.

3. Final Answer:

   Because bit manipulation works directly on binary digits using CPU instructions -> Option A

4. Quick Check:

   Bit manipulation = faster CPU-level operations [OK]

Hint: Bit ops use CPU bits directly, arithmetic uses slower math [OK]

Common Mistakes:

• Thinking bit manipulation uses more memory
• Believing arithmetic is always faster
• Confusing bit manipulation with complex algorithms

2. Which of the following TypeScript expressions correctly uses bit manipulation to multiply a number by 4?

easy

A. num & 4

B. num >> 2

C. num << 2

D. num | 4

Solution

1. Step 1: Recall bit shift left operation

   Shifting bits left by 1 multiplies the number by 2, so shifting left by 2 multiplies by 4.

2. Step 2: Check each option

   num << 2 shifts left by 2 bits, correctly multiplying by 4. num >> 2 performs right shift (division by 4), num & 4 is bitwise AND, and num | 4 is bitwise OR; none multiply by 4.

3. Final Answer:

   num << 2 -> Option C

4. Quick Check:

   Left shift by 2 = multiply by 4 [OK]

Hint: Left shift by n bits multiplies by 2^n [OK]

Common Mistakes:

• Using right shift instead of left shift
• Confusing bitwise AND/OR with multiplication
• Forgetting shift counts start at zero

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

let x = 10;
let y = x & 6;
console.log(y);

medium

A. 2

B. 6

C. 10

D. 14

Solution

1. Step 1: Convert numbers to binary

   10 in binary is 1010, 6 in binary is 0110.

2. Step 2: Perform bitwise AND

   1010 & 0110 = 0010 (binary), which is 2 in decimal.

3. Final Answer:

   2 -> Option A

4. Quick Check:

   10 & 6 = 2 [OK]

Hint: AND keeps bits set in both numbers only [OK]

Common Mistakes:

• Confusing AND with OR operation
• Not converting binary correctly
• Assuming output is decimal sum

4. Identify the error in this TypeScript code that tries to check if a number is even using bit manipulation:

function isEven(num: number): boolean {
  return (num & 1) === 1;
}

medium

A. The function is correct as is

B. The condition should check if (num & 1) === 0 to detect even numbers

C. The function should return num % 2 === 1 instead

D. Bitwise AND cannot be used to check even numbers

Solution

1. Step 1: Understand bitwise check for even numbers

   Even numbers have last bit 0, so (num & 1) equals 0 for even numbers.

2. Step 2: Analyze the condition

   The code returns true if (num & 1) === 1, which means odd numbers, so it is reversed.

3. Final Answer:

   The condition should check if (num & 1) === 0 to detect even numbers -> Option B

4. Quick Check:

   Even check = (num & 1) === 0 [OK]

Hint: Even numbers have last bit 0, check (num & 1) === 0 [OK]

Common Mistakes:

• Checking for 1 instead of 0 for even
• Thinking bitwise AND can't check parity
• Using modulo instead of bitwise unnecessarily

5. You want to quickly double a number many times in a performance-critical loop. Which approach is best and why?

function doubleManyTimes(num: number, times: number): number {
  let result = num;
  for (let i = 0; i < times; i++) {
    // Which line is best here?
    // A: result = result * 2;
    // B: result = result << 1;
  }
  return result;
}

hard

A. Use division by 0.5 (result = result / 0.5) because it's mathematically equivalent

B. Use multiplication (result = result * 2) because it's clearer

C. Use addition (result = result + result) because it's the simplest

D. Use bit shift left (result = result << 1) because it's faster and uses less CPU cycles

Solution

1. Step 1: Compare multiplication and bit shift performance

   Bit shift left is a CPU-level operation that is faster than multiplication, especially in loops.

2. Step 2: Evaluate other options

   Addition doubles but is slower than bit shift; division by 0.5 is slower and less clear.

3. Final Answer:

   Use bit shift left (result = result << 1) because it's faster and uses less CPU cycles -> Option D

4. Quick Check:

   Bit shift left = faster multiply by 2 [OK]

Hint: Use << 1 to multiply by 2 faster in loops [OK]

Common Mistakes:

• Choosing multiplication for clarity over speed
• Using addition which is slower than bit shift
• Using division which is inefficient