def gray_to_bin(gray):
    """
    Convert Gray code to binary, operating on the integer value directly.
    :returns: 32-bit String
    """
    try:
        num = int(gray, 2)  # Convert string to integer
        mask = num
        while mask != 0:
            mask >>= 1
            num ^= mask
        return format(num, '032b')  # Always return 32-bit string
    except ValueError as e:
        print(f"Error in gray_to_bin with input: '{gray}'")
        raise e

def bin_to_gray(binary):
    """
    Convert binary to Gray code using XOR with right shift
    :returns: 32-bit String
    """
    try:
        num = int(binary, 2)  # Convert string to integer
        gray = num ^ (num >> 1)  # Gray code formula: G = B ^ (B >> 1)
        return format(gray, '032b')  # Always return 32-bit string
    except ValueError as e:
        print(f"Error in bin_to_gray with input: '{binary}'")
        raise e

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]
    :returns: float 
    """
    try:
        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
    except ValueError as e:
        print(f"Error in bin_to_param with input: '{binary}'")
        raise e