import numpy as np


def project_bit(bit):
    n = len(bit)
    q_min = 0.01
    q_max = 0.5

    reverse_bit = np.flip(bit)
    dec = np.uint64(0)

    for i in range(n):
        dec += np.uint64(2)**i * reverse_bit[i]

    q = q_min + ((q_max - q_min) / (2**n - 1)) * dec 

    return q



def bit_to_grey(bit):
    grey = [bit[0]]

    for i in range(1, len(bit)):
        grey.append(bit[i-1] ^ bit[i])

    return np.array(grey)



def grey_to_bit(grey):
    bit = [grey[0]]

    for i in range(1, len(grey)):
        bit.append(bit[i-1] ^ grey[i])

    return np.array(bit)