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

Concept Flow - Bit Manipulation Basics AND OR XOR NOT Left Right Shift

Start with two numbers

↓

Apply AND (&)

→Result: bits set where both bits are 1

↓

Apply OR (|)

→Result: bits set where at least one bit is 1

↓

Apply XOR (^)

→Result: bits set where bits differ

↓

Apply NOT (~)

→Result: bits flipped

↓

Apply Left Shift (<<)

→Result: bits shifted left, zeros fill right

↓

Apply Right Shift (>>)

→Result: bits shifted right, sign bit or zero fill

↓

End

Start with two numbers, then apply bitwise AND, OR, XOR, NOT, left shift, and right shift operations step-by-step to see how bits change.

Execution Sample

DSA Python

a = 6  # 0b0110
b = 11 # 0b1011
print(a & b)
print(a | b)
print(a ^ b)
print(~a)
print(a << 1)
print(b >> 2)

This code applies bitwise AND, OR, XOR, NOT, left shift, and right shift on two numbers and prints the results.

Execution Table

Step	Operation	Operands (binary)	Result (binary)	Result (decimal)	Explanation
1	AND (&)	a=0110, b=1011	0010	2	Bits set where both bits are 1
2	OR (|)	a=0110, b=1011	1111	15	Bits set where at least one bit is 1
3	XOR (^)	a=0110, b=1011	1101	13	Bits set where bits differ
4	NOT (~)	a=0000...0110	1111...1001	-7	Bits flipped; two's complement negative
5	Left Shift (<< 1)	a=0110	1100	12	Bits shifted left by 1, zero fills right
6	Right Shift (>> 2)	b=1011	0010	2	Bits shifted right by 2, zero fills left
7	End	-	-	-	All operations completed

💡 All bitwise operations on a=6 and b=11 completed

Variable Tracker

Variable	Initial (decimal)	Initial (binary)	After AND	After OR	After XOR	After NOT (~a)	After a << 1	After b >> 2
a	6	0110	2 (0010)	15 (1111)	13 (1101)	-7 (1111...1001)	12 (1100)	3 (0011)
b	11	1011	2 (0010)	15 (1111)	13 (1101)	11 (1011)	11 (1011)	2 (0010)

Key Moments - 3 Insights

Why does the NOT (~) operation on 6 give -7 instead of a positive number?

Because NOT flips all bits including the sign bit in two's complement representation, resulting in a negative number. See step 4 in execution_table where ~6 (0000...0110) becomes 1111...1001 which is -7.

Why does left shift (<<) multiply the number by 2?

Left shift moves bits to the left, adding a zero on the right, effectively multiplying by 2 for each shift. Step 5 shows 6 (0110) shifted left once becomes 12 (1100).

What happens to bits shifted out during right shift (>>)?

Bits shifted out on the right are lost, and zeros (or sign bit for signed numbers) fill in from the left. Step 6 shows 11 (1011) shifted right twice becomes 2 (0010).

Visual Quiz - 3 Questions

Look at the execution_table, what is the result of a & b at step 1 in decimal?

A 6

B 2

C 3

D 15

💡 Hint

Check the 'Result (decimal)' column in step 1 of execution_table.

At which step does the result become negative due to bitwise operation?

A Step 5

B Step 3

C Step 4

D Step 6

💡 Hint

Look for negative decimal result in the 'Result (decimal)' column.

If we change a from 6 to 4, what would be the result of a << 1 (left shift by 1)?

A 8

B 10

C 12

D 6

💡 Hint

Left shift by 1 doubles the number; check variable_tracker for a << 1.

Concept Snapshot

Bitwise operators work on bits of numbers:
AND (&): 1 if both bits 1
OR (|): 1 if any bit 1
XOR (^): 1 if bits differ
NOT (~): flips bits, two's complement
Left Shift (<<): shifts bits left, multiplies by 2
Right Shift (>>): shifts bits right, divides by 2 (floor)

Full Transcript

This lesson shows how bitwise operations work on two numbers, 6 and 11. We apply AND, OR, XOR, NOT, left shift, and right shift step-by-step. AND keeps bits set only if both bits are 1. OR sets bits if either bit is 1. XOR sets bits where bits differ. NOT flips all bits, resulting in negative number due to two's complement. Left shift moves bits left, multiplying by 2. Right shift moves bits right, dividing by 2. We track each result in binary and decimal to see how bits change.

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