How would you reverse the bits of a given binary number?

To reverse the bits of a given binary number, we can iterate through the bits of the number from the right side, shifting the bits of the reversed number, and pushing the bit from the original number onto the reversed number. Here’s a step-by-step algorithm:

1. Set ‘reversed_number‘ to 0 (where we will collect the reversed bits)

2. While ‘number‘ is not 0, iterate:

1. Bitwise shift right ‘number‘ by 1 and set to ‘number‘. In code: ‘number >> 1‘.

2. Bitwise shift left ‘reversed_number‘ by 1 and set to ‘reversed_number‘. In code: ‘reversed_number << 1‘.

3. Get the least significant bit from ‘number‘ (bit at the rightmost side), let’s call it ‘bit‘. In code: ‘bit = number & 1‘.

4. Bitwise OR ‘reversed_number‘ with ‘bit‘, and set to ‘reversed_number‘. In code: ‘reversed_number = reversed_number | bit‘.

In Python, the explained algorithm would look like this:

def reverse_bits(number):
    reversed_number = 0
    while number != 0:
        number = number >> 1
        reversed_number = reversed_number << 1
        bit = number & 1
        reversed_number = reversed_number | bit
    return reversed_number

Let’s take an example where the input binary number is 12 (in binary 1100):

1. Initially, reversed_number=0 (in binary 0).

2. In the first iteration, we right shift number by 1, making it 6 (110).

3. Now we left shift the reversed_number by 1, it remains 0.

4. Extract the last bit of number, which is 0.

5. OR operation between reversed_number (0) and bit (0) remains 0.

6. In the next iteration, number becomes 3 (11), and reversed_number is still 0.

7. Bit extraction from number gives us 1 this time.

8. OR operation between reversed_number (0) and bit (1) gives us 1.

9. After a few more iterations, the original number becomes 0, and the reversed_number becomes 3 (in binary 0011), which is the reverse of initial binary 1100.

An important note: this algorithm assumes that the inputs and outputs fit in a designated number of bits (like 32 bits for int in Python). If you could potentially have large integers that are over 32 bits, you’d need to modify the algorithm to accommodate that.