Is it possible to do bit reversal for a 16 bit number only using shift left, xor, and bitwise operations on python

Question

I was wondering if it is possible to do bit reversal for a 16bit binary number such as 1000000000000011 to 1100000000000001 by only using the shift left >>, Xor ^, And & functions on python? Adding and subtracting binary can also be used for this problem

Answer 1

The description you give in the comments for "left shift" is not what Python does for << - you're describing what would be called a "left rotate". Since Python doesn't provide that, let's code it up quick:

def circular_shift_16(x, n):
    assert(0 <= x <= 0xffff)
    return (( x << n) & 0xffff) | (x >> (16-n))

With that as a building block, you can do the bit reversal.

def bit_reversal_16(x):
    # reverse single bit pairs
    x = (circular_shift_16(x, 15) & 0x5555) ^ (circular_shift_16(x, 1) & 0xaaaa)
    # reverse groups of 2
    x = (circular_shift_16(x, 14) & 0x3333) ^ (circular_shift_16(x, 2) & 0xcccc)
    # reverse groups of 4
    x = (circular_shift_16(x, 12) & 0x0f0f) ^ (circular_shift_16(x, 4) & 0xf0f0)
    # reverse groups of 8
    x = circular_shift_16(x, 8)
    return x