Bit Manipulation Basics AND OR XOR NOT Left Right Shift in DSA Python - 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.

intermediate

Describe the NOT (~) bitwise operator.

NOT flips each bit: 1 becomes 0, and 0 becomes 1.
Example: ~1 (in 1-bit) = 0, ~0 = 1.
In computers, it also changes the sign due to two's complement representation.

intermediate

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

Left shift (<<) moves bits to the left, adding zeros on the right, effectively multiplying by 2 for each shift.
Right shift (>>) moves bits to the right, discarding bits on the right, effectively dividing by 2 for each shift.
Example: 4 (0100) << 1 = 8 (1000), 4 >> 1 = 2 (0010).

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

A 0101 (5)

B 0011 (3)

C 0001 (1)

D 0111 (7)

AND compares bits: 0&0=0,1&1=1, so 0101 & 0011 = 0001 which is 1.

Which operator returns 1 only when bits are different?

A AND (&)

B NOT (~)

C OR (|)

D XOR (^)

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

What does the expression ~0 evaluate to in a 4-bit system?

A 1111 (-1 in two's complement)

B 0000 (0)

C 1110 (14)

D 0001 (1)

NOT flips all bits: ~0000 = 1111, which is -1 in two's complement.

What is the decimal result of 6 << 2?

A 24

B 12

C 3

D 48

Left shift by 2 multiplies by 2^2=4, so 6*4=24.

Which bitwise operator would you use to clear specific bits (set them to 0)?

A OR (|) with mask

B AND (&) with mask

C XOR (^) with mask

D NOT (~)

AND with a mask having 0s clears bits; 1s keep bits unchanged.

Explain how the XOR operator works and give a real-life example where it might be useful.

Think about switching a light on/off using XOR.

Describe what happens to a binary number when you perform a left shift and a right shift.

Imagine moving digits in a number to the left or right.

Practice

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

easy

A. 1

B. 7

C. 6

D. 0

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 AND 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 AND

2. Which of the following is the correct syntax to perform a left shift by 2 bits on variable x in Python?

easy

A. x <<< 2

B. x >> 2

C. x << 2

D. x >>| 2

Solution

1. Step 1: Understand left shift operator in Python

   Left shift is done using << operator, shifting bits to the left.

2. Step 2: Check syntax options

   Only x << 2 correctly shifts bits left by 2 places.

3. Final Answer:

   x << 2 -> Option C

4. Quick Check:

   Left shift uses << operator [OK]

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

Common Mistakes:

• Using >>> which is not valid in Python
• Confusing left shift with right shift operator
• Using invalid operators like >>|

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

num = 12  # binary 1100
result = num >> 2
print(result)

medium

A. 6

B. 0

C. 48

D. 3

Solution

1. Step 1: Convert number and apply right shift

   12 in binary is 1100. Right shifting by 2 bits removes last two bits: 1100 >> 2 = 0011.

2. Step 2: Convert shifted binary back to decimal

   0011 in binary is 3 in decimal.

3. Final Answer:

   3 -> Option D

4. Quick Check:

   12 >> 2 = 3 [OK]

Hint: Right shift divides number by 2^shift count [OK]

Common Mistakes:

• Confusing right shift with left shift
• Not converting binary back to decimal
• Assuming shift multiplies instead of divides

4. Identify the error in the following code snippet:

value = 10
result = ~value << 1
print(result)

medium

A. Result is -22 due to operator precedence

B. RuntimeError due to invalid shift

C. Result is 21 due to incorrect bitwise NOT

D. SyntaxError due to incorrect operator usage

Solution

1. Step 1: Evaluate bitwise NOT and shift

   ~10 equals -11 (because ~x = -x-1). Then shifting left by 1 bit multiplies by 2: -11 << 1 = -22.

2. Step 2: Check operator precedence and final value

   Because ~ has higher precedence, ~10 is evaluated first, then shifted. So result is -22, but print shows -22.

3. Final Answer:

   Result is -22 due to operator precedence -> Option A

4. Quick Check:

   ~10 << 1 = -22 [OK]

Hint: Bitwise NOT flips bits, watch operator precedence [OK]

Common Mistakes:

• Assuming ~10 is positive
• Ignoring operator precedence between ~ and <<
• Expecting shift to apply before NOT

5. Given two integers a = 9 and b = 14, which expression will toggle the bits where a and b differ?

hard

A. a | b

B. a ^ b

C. a & b

D. ~a

Solution

1. Step 1: Understand toggling bits where numbers differ

   Toggling bits means flipping bits that are different between two numbers.

2. Step 2: Identify bitwise XOR operation

   XOR (^) returns 1 where bits differ and 0 where bits are same, effectively toggling differing bits.

3. Final Answer:

   a ^ b -> Option B

4. Quick Check:

   XOR toggles differing bits [OK]

Hint: XOR flips bits where inputs differ [OK]

Common Mistakes:

• Using AND or OR which do not toggle bits
• Confusing NOT (~) with XOR
• Assuming OR toggles bits