Reverse Bits

Reverse the 32 bits of an unsigned integer.

Start with the concrete trace below. It shows the state the algorithm must carry as it runs.

Problem trace

Reverse Bits: Across exactly 32 iterations, consume input bits from least significant to most significant and append each bit to the growing answer.

Input and goalReverse the 32 bits of an unsigned integer.

Initialize the 32-bit wordInput 43261596 is 00000010100101000001111010011100₂. Set answer = 0 before reading bit position 0.

00010203040516071809010111012113014015016017018119120121122023124025026127128129030next: bit 0031

input43261596value00000010100101000001111010011100answer00000000000000000000000000000000

Recognize it

The task reverses all 32 positions, including leading zeros, so processing must run a fixed number of times rather than stopping when the numeric input becomes zero.

Keep true

After k iterations, answer contains the original k least-significant bits in reverse read order, while value contains the original bits not yet consumed after k right shifts.

Reuse it

For fixed-width encodings, separate reading order from numeric termination: consume one boundary unit, shift the destination, append, and repeat for the declared width. The pattern transfers to radix conversion and stream packing.

Pattern: Read from one end and build at the other.

Simple idea: Read the last input bit, append it to the answer, then shift the input right. Repeat exactly 32 times.

def reverse_bits(value: int) -> int:
   answer = 0
   for _ in range(32):
      answer = (answer << 1) | (value & 1)
      value >>= 1
   return answer

Cost: $O(1)$ time and space for 32 bits.