Bit Manipulation Basics AND OR XOR NOT Left Right Shift in DSA Javascript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does the AND (&) bitwise operator do between two bits?

It returns 1 only if both bits are 1; otherwise, it returns 0.
Example: 1 & 1 = 1, 1 & 0 = 0, 0 & 0 = 0.

beginner

Explain the OR (|) bitwise operator with a simple example.

OR returns 1 if at least one of the bits is 1; otherwise, it returns 0.
Example: 1 | 0 = 1, 0 | 0 = 0, 1 | 1 = 1.

beginner

What is the result of XOR (^) between two bits?

XOR returns 1 if the bits are different, and 0 if they are the same.
Example: 1 ^ 0 = 1, 1 ^ 1 = 0, 0 ^ 0 = 0.

beginner

Describe the NOT (~) bitwise operator and its effect on a bit.

NOT flips the bit: 0 becomes 1, and 1 becomes 0.
Example: ~0 = 1, ~1 = 0 (in single bit context).

beginner

What happens when you perform a left shift (<<) on a binary number?

Left shift moves all bits to the left by the given number of positions, adding zeros on the right.
It effectively multiplies the number by 2 for each shift.
Example: 0010 (2) << 1 = 0100 (4).

What is the result of 5 & 3 in binary? (5 = 0101, 3 = 0011)

A 0010 (2)

B 0111 (7)

C 0001 (1)

D 0100 (4)

AND compares bits: 0101 & 0011 = 0001, which is 1 in decimal.

Which operator returns 1 only when bits are different?

A OR (|)

B XOR (^)

C AND (&)

D NOT (~)

XOR returns 1 if bits differ, 0 if they are the same.

What does the right shift (>>) operator do?

A Moves bits to the left, adding zeros on the right

B Flips all bits

C Moves bits to the right, discarding bits on the right

D Moves bits to the right, adding zeros on the left

Right shift moves bits right, adding zeros on the left (logical right shift).

What is the result of ~0 in a 4-bit system?

A 1111

B 0000

C 1000

D 0111

NOT flips all bits: ~0000 = 1111 in 4 bits.

Which bitwise operator would you use to set a specific bit to 1?

A OR (|)

B NOT (~)

C XOR (^)

D AND (&)

OR with 1 sets the bit to 1 without changing others.

Explain how the AND, OR, and XOR bitwise operators work with examples.

Think about how bits combine in each operator.

Describe what happens when you perform left and right bit shifts on a binary number.

Imagine moving bits like sliding blocks left or right.

Practice

1. What is the result of the bitwise AND operation between 5 and 3? (5 & 3)

easy

A. 1

B. 7

C. 0

D. 8

Solution

1. Step 1: Convert numbers to binary

   5 in binary is 0101, 3 in binary is 0011.

2. Step 2: Perform bitwise AND

   0101 & 0011 = 0001 (only bits set in both numbers remain set).

3. Final Answer:

   1 -> Option A

4. Quick Check:

   5 & 3 = 1 [OK]

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

Common Mistakes:

• Confusing AND with OR operation
• Not converting numbers to binary before operation
• Assuming decimal addition instead of bitwise

2. Which of the following is the correct syntax for performing a bitwise XOR operation between variables a and b in JavaScript?

easy

A. let result = a | b;

B. let result = a && b;

C. let result = a % b;

D. let result = a ^ b;

Solution

1. Step 1: Identify bitwise XOR operator in JavaScript

   The XOR operator is represented by the caret symbol (^).

2. Step 2: Check syntax correctness

   let result = a ^ b; uses a ^ b, which is the correct syntax for bitwise XOR.

3. Final Answer:

   let result = a ^ b; -> Option D

4. Quick Check:

   XOR operator is ^ in JavaScript [OK]

Hint: XOR uses ^ symbol in JavaScript [OK]

Common Mistakes:

• Using && which is logical AND, not bitwise
• Using | which is bitwise OR, not XOR
• Using % which is modulo, unrelated to bits

3. What will be the output of the following JavaScript code?

let x = 8; // binary 1000
let y = x >> 2;
console.log(y);

medium

A. 2

B. 4

C. 1

D. 0

Solution

1. Step 1: Understand right shift operation

   Right shift by 2 means move bits 2 places to the right, dropping the rightmost bits.

2. Step 2: Apply right shift on binary 1000

   1000 >> 2 becomes 0010, which is decimal 2.

3. Final Answer:

   2 -> Option A

4. Quick Check:

   8 >> 2 = 2 [OK]

Hint: Right shift divides by 2 for each shift [OK]

Common Mistakes:

• Confusing right shift with left shift
• Not converting binary to decimal after shift
• Assuming shift adds zeros on left without dropping bits

4. Find the error in the following code snippet that attempts to flip all bits of a number n using bitwise NOT:

let n = 5;
let flipped = ~n;
console.log(flipped);

What is the issue?

medium

A. Missing parentheses around ~n

B. Bitwise NOT returns a negative number due to two's complement representation

C. Variable n must be a string for bitwise NOT

D. Bitwise NOT operator (~) is not supported in JavaScript

Solution

1. Step 1: Understand bitwise NOT in JavaScript

   Bitwise NOT flips all bits and returns the two's complement negative number.

2. Step 2: Explain why output is negative

   For 5 (00000101), ~5 flips bits to 11111010 which is -6 in two's complement.

3. Final Answer:

   Bitwise NOT returns a negative number due to two's complement representation -> Option B

4. Quick Check:

   ~n flips bits and returns negative number [OK]

Hint: Bitwise NOT flips bits and returns negative in JS [OK]

Common Mistakes:

• Expecting positive flipped bits as output
• Thinking ~ is unsupported operator
• Assuming input must be string for bitwise ops

5. You want to set the 3rd bit (0-indexed from right) of a number num to 1 without changing other bits. Which expression correctly does this in JavaScript?

hard

A. num = num ^ (1 << 3);

B. num = num & (1 << 3);

C. num = num | (1 << 3);

D. num = num << 3;

Solution

1. Step 1: Understand setting a bit using OR and shift

   Left shift 1 by 3 gives 00001000, which targets the 3rd bit.

2. Step 2: Use OR to set the bit without changing others

   OR with this mask sets the 3rd bit to 1, keeping others unchanged.

3. Final Answer:

   num = num | (1 << 3); -> Option C

4. Quick Check:

   Use OR with shifted 1 to set bit [OK]

Hint: Use OR with (1 << bit_position) to set bit [OK]

Common Mistakes:

• Using AND which clears bits instead of setting
• Using XOR which toggles bits and may unset
• Using left shift alone which changes number value