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

Recall & Review

beginner

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

The AND operator 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 an example.

The OR operator 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

What does the NOT (~) operator do to a bit?

The NOT operator flips the bit: 1 becomes 0, and 0 becomes 1.
Example: ~1 = 0, ~0 = 1 (in binary representation).

beginner

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

Left shift moves all bits to the left by the given number of positions, adding zeros on the right.
This is like multiplying the number by 2 for each shift.
Example: 3 (011) << 1 = 6 (110).

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

A 0100

B 0111

C 0001

D 0010

5 & 3 = 0101 & 0011 = 0001.

Which operator flips all bits of a number?

A OR (|)

B NOT (~)

C AND (&)

D XOR (^)

NOT (~) flips all bits: 1 becomes 0 and 0 becomes 1.

What does the expression (6 >> 1) evaluate to? (6 = 0110 in binary)

A 0001 (1)

B 1100 (12)

C 0110 (6)

D 0011 (3)

Right shift by 1 moves bits right, dropping the last bit: 0110 >> 1 = 0011 (3).

What is the result of 4 ^ 4?

A 0

B 4

C 8

D 1

XOR of a number with itself is always 0.

Which bitwise operator returns 1 if either bit is 1?

A OR (|)

B XOR (^)

C AND (&)

D NOT (~)

OR (|) returns 1 if at least one bit is 1.

Describe how the AND, OR, XOR, and NOT bitwise operators work with simple examples.

Think about how each operator treats pairs of bits.

Explain what happens when you perform left shift (<<) and right shift (>>) on a binary number.

Imagine sliding bits left or right in a row.

Practice

1. What is the result of the bitwise AND operation between 5 and 3? (5 = 0101, 3 = 0011 in binary)

easy

A. 0

B. 1

C. 6

D. 7

Solution

1. Step 1: Convert numbers to binary

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

2. Step 2: Perform bitwise AND operation

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

3. Final Answer:

   1 -> Option B

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 decimal to binary correctly
• Mixing bit positions during calculation

2. Which of the following is the correct syntax for left shifting the integer x by 2 bits in C?

easy

A. x >> 2;

B. x <<< 2;

C. x << 2;

D. x >> 2 <<;

Solution

1. Step 1: Understand left shift operator in C

   The left shift operator is written as << and shifts bits to the left.

2. Step 2: Check syntax correctness

   x << 2; uses x << 2; which correctly shifts bits of x left by 2 positions.

3. Final Answer:

   x << 2; -> Option C

4. Quick Check:

   Left shift syntax = x << 2; [OK]

Hint: Use << for left shift, >> for right shift [OK]

Common Mistakes:

• Using >>> which is invalid in C
• Confusing left shift with right shift
• Incorrect operator placement or syntax

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

int x = 6; // binary 0110
int y = x ^ 3; // 3 = 0011
printf("%d", y);

medium

A. 9

B. 7

C. 1

D. 5

Solution

1. Step 1: Convert numbers to binary and apply XOR

   6 in binary is 0110, 3 is 0011. XOR operation: 0110 ^ 0011 = 0101.

2. Step 2: Calculate decimal value of XOR result

   0101 in binary equals 5 decimal.

3. Final Answer:

   5 -> Option D

4. Quick Check:

   6 ^ 3 = 5 [OK]

Hint: XOR flips bits where bits differ [OK]

Common Mistakes:

• Mixing XOR with OR or AND
• Incorrect binary conversion
• Misreading bit positions

4. Identify the error in the following C code snippet:

int x = 8;
int y = ~x << 1;
printf("%d", y);

medium

A. Using ~ operator without parentheses causes wrong shift

B. Missing semicolon after declaration

C. Shift operator << cannot be used with ~ operator

D. No error, code runs correctly

Solution

1. Step 1: Understand operator precedence

   The bitwise NOT (~) has higher precedence than shift (<<), so ~x is evaluated first.

2. Step 2: Check if parentheses needed

   Without parentheses, ~x is computed, then shifted left. This is correct but may cause confusion if intended differently.

3. Step 3: Identify common mistake

   If intention was to shift x first then NOT, parentheses are needed. Otherwise, no syntax error but logic may be wrong.

4. Final Answer:

   Using ~ operator without parentheses causes wrong shift -> Option A

5. Quick Check:

   Operator precedence matters; use parentheses [OK]

Hint: Use parentheses to control bitwise operation order [OK]

Common Mistakes:

• Ignoring operator precedence
• Assuming shift applies before NOT
• Thinking code has syntax error when it doesn't

5. Given an integer n, which expression correctly checks if the 3rd bit (from right, zero-based) is set (1)?

hard

A. (n & (1 << 3)) != 0

B. (n | (1 << 3)) == 0

C. (n ^ (1 << 3)) == 0

D. (n >> 3) & 1 == 0

Solution

1. Step 1: Understand bit position and mask

   The 3rd bit (zero-based) means bit at position 3. Mask is 1 shifted left by 3: (1 << 3) = 8.

2. Step 2: Check if bit is set using AND

   Using (n & (1 << 3)) checks if that bit is 1. If result is not zero, bit is set.

3. Final Answer:

   (n & (1 << 3)) != 0 -> Option A

4. Quick Check:

   Bit check uses AND with mask [OK]

Hint: Use AND with (1 << bit_position) to check bit [OK]

Common Mistakes:

• Using OR or XOR instead of AND for checking
• Wrong bit position shift
• Comparing shifted bit to zero incorrectly