import matplotlib.pyplot as plt
import numpy as np
import scipy.interpolate as interpolate

def gray_to_bin(gray):
    """
    Convert Gray code to binary, operating on the integer value directly.
    :returns: 32-bit String
    """
    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

def bin_to_param(binary, q_min = 0.0, q_max = 5.0):
    """
    Convert one binary string to float parameter in range [q_min, q_max]
    :returns: float 
    """
    val = int(binary, 2) / 25.5 * 10.0 # conversion to 0.0 - 10.0
    # Scale to range [q_min, q_max]
    q = q_min + ((q_max - q_min) / (2**len(binary))) * val
    return q

def plot_graph(a, b, c, d): 
    x = np.arange(-1., 1., 0.1)
    
    fig, ax = plt.subplots()
    y_approx = a*x**3 + b*x**2 + c*x + d
    y_exact = np.e**x
    y_taylor = interpolate.approximate_taylor_polynomial(np.exp, 0, 3, 1)(x)
    ax.plot(x, y_approx, label='approx. func.')
    ax.plot(x, y_taylor, label='taylor')
    ax.plot(x, y_exact, label='e^x')
    ax.set_xlim(-1, 1)
    ax.set_ylim(-1, 5)
    plt.legend()
    plt.show()