def grey_to_bin(gray):
    """Convert Gray code to binary, operating on the integer value directly"""
    num = int(gray, 2)  # Convert string to integer
    mask = num
    while mask != 0:
        mask >>= 1
        num ^= mask
    return format(num, f'0{len(gray)}b')  # Convert back to binary string with same length

def bin_to_grey(binary):
    """Convert binary to Gray code using XOR with right shift"""
    num = int(binary, 2)  # Convert string to integer
    gray = num ^ (num >> 1)  # Gray code formula: G = B ^ (B >> 1)
    return format(gray, f'0{len(binary)}b')  # Convert back to binary string with same length

def bin_to_param(binary, q_min = 0.0, q_max = 10.0):
    """Convert one binary string to float parameter in range [q_min, q_max]"""
    val = int(binary, 2) / 25.5 * 10 # conversion to 0.0 - 10.0 float
    # Scale to range [q_min, q_max]
    q = q_min + ((q_max - q_min) / (2**len(binary))) * val
    
    return q