Reverse Bits of a Number in DSA Java - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does it mean to reverse the bits of a number?

Reversing the bits means flipping the order of all bits in the binary form of the number, so the first bit becomes the last, the second becomes the second last, and so on.

beginner

Why do we use bitwise operations to reverse bits instead of string operations?

Bitwise operations work directly on the binary representation and are faster and use less memory than converting to strings and reversing.

beginner

In Java, which operator is used to shift bits to the right?

The '>>' operator shifts bits to the right, filling with the sign bit, and '>>>' shifts bits to the right filling with zero.

beginner

What is the purpose of using '& 1' in bit manipulation?

Using '& 1' extracts the least significant bit (rightmost bit) of a number, which helps in checking if it is 0 or 1.

beginner

How many bits do we usually consider when reversing bits of an integer in Java?

We usually consider 32 bits because Java's int type is 32 bits long.

What is the result of reversing bits of the number 1 (binary 000...0001) in 4 bits?

A 8 (binary 1000)

B 1 (binary 0001)

C 4 (binary 0100)

D 0 (binary 0000)

Reversing 0001 in 4 bits gives 1000, which is 8 in decimal.

Which bitwise operator shifts bits to the left in Java?

A &

B >>

C >>>

D <<

The '<<' operator shifts bits to the left, adding zeros on the right.

What does the expression 'n & 1' check in bit manipulation?

A If n is even or odd

B If n is positive or negative

C If n is zero

D If n is a power of two

'n & 1' checks the least significant bit, which tells if n is even (0) or odd (1).

How many bits are reversed when reversing bits of an int in Java?

A 8 bits

B 32 bits

C 16 bits

D 64 bits

Java int is 32 bits, so reversing bits means reversing all 32 bits.

Which of these is the correct way to get the rightmost bit of a number n?

A n >> 1

B n << 1

C n & 1

D n | 1

'n & 1' extracts the rightmost bit of n.

Explain step-by-step how to reverse the bits of a 32-bit integer using bitwise operations.

Think about moving bits from right to left one by one.

Why is reversing bits useful in programming? Give two examples.

Think about where bit order matters.

Practice

1. What does reversing the bits of a number mean in simple terms?

easy

A. Shifting bits to the left by one position

B. Flipping the order of bits from left to right

C. Adding 1 to the number

D. Changing all bits from 0 to 1

Solution

1. Step 1: Understand bit order

   Bits are the 0s and 1s that make up a number. Reversing means flipping their order.

2. Step 2: Explain reversing bits

   If the bits are 1010, reversing them gives 0101, flipping left to right.

3. Final Answer:

   Flipping the order of bits from left to right -> Option B

4. Quick Check:

   Reverse bits = flip order [OK]

Hint: Think of bits like beads on a string flipped end to end [OK]

Common Mistakes:

• Confusing reversing bits with flipping bits (0 to 1)
• Thinking reversing means adding or subtracting
• Mixing bit shifting with bit reversing

2. Which Java syntax correctly reverses bits of an integer n using a loop?

easy

A. for (int i = 0; i < 32; i++) { result <<= 1; result |= (n & 1); n >>= 1; }

B. for (int i = 0; i < 32; i++) { result |= (n & 1) << i; n >>= 1; }

C. for (int i = 0; i < 32; i++) { result += (n & 1) << i; n <<= 1; }

D. for (int i = 0; i < 32; i++) { result <<= 1; result |= (n >> i) & 1; }

Solution

1. Step 1: Analyze bit extraction and shifting

   for (int i = 0; i < 32; i++) { result <<= 1; result |= (n & 1); n >>= 1; } extracts the least significant bit (n & 1), shifts result left, then adds the bit, and shifts n right.

2. Step 2: Check correctness of loop operations

   for (int i = 0; i < 32; i++) { result <<= 1; result |= (n & 1); n >>= 1; } correctly reverses bits by building result from left to right while moving through n's bits right to left.

3. Final Answer:

   for (int i = 0; i < 32; i++) { result <<= 1; result |= (n & 1); n >>= 1; } -> Option A

4. Quick Check:

   Shift result left, add bit from n, shift n right [OK]

Hint: Shift result left before adding extracted bit [OK]

Common Mistakes:

• Shifting n left instead of right
• Adding bits without shifting result
• Using incorrect bit extraction

3. What is the output of this Java code snippet?

int n = 13; // binary 00000000000000000000000000001101
int result = 0;
for (int i = 0; i < 4; i++) {
  result <<= 1;
  result |= (n & 1);
  n >>= 1;
}
System.out.println(result);

medium

A. 11

B. 13

C. 7

D. 14

Solution

1. Step 1: Trace each loop iteration

   Initial n=13 (binary 1101). Loop runs 4 times:
   i=0: result=0<<1=0; result|=1 (n&1=1); result=1; n=6
   i=1: result=1<<1=2; result|=0 (6&1=0); result=2; n=3
   i=2: result=2<<1=4; result|=1 (3&1=1); result=5; n=1
   i=3: result=5<<1=10; result|=1 (1&1=1); result=11; n=0

2. Step 2: Convert final result to decimal

   Result is 11 decimal after reversing 4 bits of 13.

3. Final Answer:

   11 -> Option A

4. Quick Check:

   Reversed 1101 bits = 1011 = 11 decimal [OK]

Hint: Reverse bits step-by-step, track result and n carefully [OK]

Common Mistakes:

• Not limiting loop to 4 bits
• Mixing bit order in result
• Confusing decimal and binary values

4. Find the error in this Java code that tries to reverse bits of a 8-bit number n:

int result = 0;
for (int i = 0; i <= 8; i++) {
  result <<= 1;
  result |= (n & 1);
  n >>= 1;
}

medium

A. Result should be shifted right, not left

B. Bitwise OR operator is used incorrectly

C. Loop runs one extra time causing wrong result

D. Variable n should not be shifted inside the loop

Solution

1. Step 1: Check loop range for 8 bits

   The loop runs from i=0 to i=8 inclusive, which is 9 iterations, but 8 bits need only 8 iterations.

2. Step 2: Understand effect of extra iteration

   Extra iteration shifts result one more time and adds an extra bit, causing incorrect reversed value.

3. Final Answer:

   Loop runs one extra time causing wrong result -> Option C

4. Quick Check:

   Loop should run 8 times, not 9 [OK]

Hint: Use < 8, not <= 8 for 8-bit loops [OK]

Common Mistakes:

• Using <= instead of < in loop condition
• Shifting result right instead of left
• Not shifting n inside loop

5. Given a 16-bit unsigned integer, how would you reverse its bits and return the result in Java? Which approach is best?

hard

A. Shift n left 16 times and OR with result

B. Convert number to binary string, reverse string, parse back to int

C. Use recursion to reverse bits one by one without loops

D. Use a loop shifting result left and extracting bits from n right, running 16 times

Solution

1. Step 1: Consider efficiency and correctness

   Looping 16 times, shifting result left and extracting bits from n right is efficient and direct for 16-bit reversal.

2. Step 2: Evaluate other options

   Converting to string is slower and error-prone; recursion adds overhead; shifting n left 16 times loses bits.

3. Final Answer:

   Use a loop shifting result left and extracting bits from n right, running 16 times -> Option D

4. Quick Check:

   Loop + bit shifts = best for fixed bit reversal [OK]

Hint: Loop 16 times, shift result left, add n's right bit [OK]

Common Mistakes:

• Using string conversion for bit operations
• Recursion without base case or efficiency
• Shifting n left losing original bits