Why Reverse Bits of a Number in DSA Go?

The Big Idea

What if flipping the order of bits could be done as easily as flipping a switch?

The Scenario

Imagine you have a number represented in binary, like a row of light switches that can be on or off. You want to flip the order of these switches so the first becomes last and the last becomes first.

Doing this by hand means checking each switch one by one and moving it to the opposite end, which is slow and confusing.

The Problem

Manually reversing bits means looking at each bit, remembering its position, and placing it in the new position. This is error-prone and takes a lot of time, especially for large numbers.

It's like trying to reverse a long string of beads one by one without a tool -- easy to lose track or make mistakes.

The Solution

Using a simple algorithm, we can automatically reverse the bits by shifting and masking bits in a loop. This method is fast, reliable, and works for any number size.

It's like having a machine that flips the entire row of switches perfectly in one go.

Before vs After

✗ Before

var reversed uint32 = 0
for i := 0; i < 32; i++ {
  bit := (num >> i) & 1
  reversed |= bit << (31 - i)
}

✓ After

func reverseBits(num uint32) uint32 {
  var reversed uint32 = 0
  for i := 0; i < 32; i++ {
    reversed <<= 1
    reversed |= num & 1
    num >>= 1
  }
  return reversed
}

What It Enables

This lets us quickly and correctly reverse the bit order of any number, enabling tasks like data encoding, cryptography, and low-level hardware control.

Real Life Example

In network communication, reversing bits is used to convert data between different formats or protocols that expect bits in opposite orders.

Key Takeaways

Manual bit reversal is slow and error-prone.

Algorithmic bit reversal uses shifting and masking to automate the process.

This operation is essential in systems programming and data processing.

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 0s to 1s and 1s to 0s

Solution

1. Step 1: Understand bit representation

   Numbers are stored as bits (0s and 1s) in a sequence from left (most significant) to right (least significant).

2. Step 2: Define reversing bits

   Reversing bits means taking the bit sequence and flipping it so the first bit becomes last, second becomes second last, and so on.

3. Final Answer:

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

4. Quick Check:

   Reverse bits = flip order [OK]

Hint: Reverse bits means flip their order, not flip values [OK]

Common Mistakes:

• Confusing reversing bits with bitwise NOT (flip 0s and 1s)
• Thinking reversing bits means adding or subtracting
• Mixing reversing bits with shifting bits

2. Which Go code snippet correctly reverses bits of a 8-bit unsigned integer n?

easy

A. var rev uint8 = 0
for i := 0; i < 8; i++ {
rev = rev >> 1
rev |= n & 1
n <<= 1
}

B. var rev uint8 = 0
for i := 0; i < 8; i++ {
rev |= (n & 1) << i
n >>= 1
}

C. var rev uint8 = 0
for i := 0; i < 8; i++ {
rev += n & 1
n <<= 1
}

D. var rev uint8 = 0
for i := 0; i < 8; i++ {
rev <<= 1
rev |= n & 1
n >>= 1
}

Solution

1. Step 1: Analyze bit reversal logic

   We shift rev left to make space, add the least significant bit of n, then shift n right to process next bit.

2. Step 2: Check code correctness

   var rev uint8 = 0 for i := 0; i < 8; i++ { rev <<= 1 rev |= n & 1 n >>= 1 } correctly shifts rev left, ORs with n's last bit, then shifts n right. Others either shift wrong direction or add bits incorrectly.

3. Final Answer:

   The code in A correctly reverses bits -> Option D

4. Quick Check:

   Shift rev left + add n's LSB + shift n right = correct [OK]

Hint: Shift rev left, add n's last bit, shift n right each loop [OK]

Common Mistakes:

• Shifting rev right instead of left
• Shifting n left instead of right
• Adding bits without shifting rev

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

func reverseBits(n uint8) uint8 {
  var rev uint8 = 0
  for i := 0; i < 8; i++ {
    rev <<= 1
    rev |= n & 1
    n >>= 1
  }
  return rev
}

fmt.Println(reverseBits(13))

Note: 13 in binary is 00001101.

medium

A. 176

B. 11

C. 101

D. 208

Solution

1. Step 1: Convert 13 to binary and reverse bits

   13 in 8 bits: 00001101. Reversing bits: 10110000.

2. Step 2: Convert reversed bits back to decimal

   10110000 binary = 128 + 32 + 16 = 176 decimal.

3. Final Answer:

   176 -> Option A

4. Quick Check:

   Reverse(00001101) = 10110000 = 176 [OK]

Hint: Reverse bits visually, then convert binary to decimal [OK]

Common Mistakes:

• Confusing bit order and reversing incorrectly
• Calculating decimal from wrong binary
• Ignoring leading zeros in 8-bit representation

4. Find the error in this Go function that tries to reverse bits of a 4-bit number:

func reverse4Bits(n uint8) uint8 {
  var rev uint8 = 0
  for i := 0; i < 4; i++ {
    rev |= (n & 1) << i
    n >>= 1
  }
  return rev
}

medium

A. The shift operator should be >> instead of <<

B. The loop should run 8 times for 4-bit numbers

C. The bits are not reversed; they are copied in the same order

D. Variable rev should be int, not uint8

Solution

1. Step 1: Understand the code logic

   The code shifts bits of n right, then sets rev bits by shifting left by i, which copies bits in same order.

2. Step 2: Identify why bits are not reversed

   Reversing bits requires shifting rev left each time and adding n's last bit, not shifting by i.

3. Final Answer:

   The bits are not reversed; they are copied in the same order -> Option C

4. Quick Check:

   Shifting rev by i copies bits, not reverses [OK]

Hint: Shift rev left each loop to reverse bits, not shift by i [OK]

Common Mistakes:

• Confusing bit copying with reversing
• Wrong loop count for bit size
• Incorrect variable types for bits

5. You want to reverse bits of a 16-bit unsigned integer and then check if the reversed number is a palindrome in binary (reads same forwards and backwards). Which approach is correct?

hard

A. Reverse bits using a loop, then compare reversed number with original

B. Reverse bits using a loop, then reverse again and compare with original

C. Check if original number equals reversed number without reversing bits

D. Shift bits left and right alternately without reversing

Solution

1. Step 1: Reverse bits of the number

   Use a loop to reverse all 16 bits to get reversed number.

2. Step 2: Check if reversed number is a palindrome

   To verify if reversed reads the same forwards and backwards, compute reverse(reversed) and check if it equals reversed. Since reverse(reversed) = original, this is equivalent to comparing reversed with original.

3. Final Answer:

   Reverse bits using a loop, then compare reversed number with original -> Option A

4. Quick Check:

   reversed == original iff reversed is palindrome [OK]

Hint: Reverse once, then compare reversed with original [OK]

Common Mistakes:

• Double reversing and comparing to original (always true, doesn't check palindrome)
• Trying to check equality without computing the reverse
• Using shifting without proper bit reversal