modules/numbering_system/conversion_bases.py

import random
import sympy as sp

title = "Conversion Between Bases"
description = "This module covers conversion techniques between different bases, including with and without fractions."

def generate_question():
    # Choose a base and corresponding valid digits, ensuring from_base and to_base are not the same
    from_base = random.choice([2, 8, 10, 16])
    to_base = random.choice([b for b in [2, 8, 10, 16] if b != from_base])

    digits = '01' if from_base == 2 else '01234567' if from_base == 8 else '0123456789' if from_base == 10 else '0123456789ABCDEF'

    # Generate a valid number for the selected from_base
    number = ''.join(random.choice(digits) for _ in range(4))

    def convert_number(number, from_base, to_base):
        # Convert from `from_base` to base 10 using Python's built-in `int`
        base_10_value = int(number, from_base)
        # Convert from base 10 to `to_base` using Python's built-in methods
        if to_base == 10:
            return str(base_10_value), base_10_value
        elif to_base == 16:
            return hex(base_10_value)[2:].upper(), base_10_value
        elif to_base == 8:
            return oct(base_10_value)[2:], base_10_value
        elif to_base == 2:
            return bin(base_10_value)[2:], base_10_value

    correct_answer, base_10_value = convert_number(number, from_base, to_base)
    options = [correct_answer]

    # Generate incorrect answers
    while len(options) < 4:
        invalid_number = ''.join(random.choice(digits) for _ in range(4))
        invalid_answer, _ = convert_number(invalid_number, from_base, to_base)
        if invalid_answer not in options:
            options.append(invalid_answer)
    
    random.shuffle(options)
    
    question = f"Convert the number {number} from base {from_base} to base {to_base}."
    explanation = f"The number {number} in base {from_base} is {correct_answer} in base {to_base}."
    
    # Step-by-step solution using SymPy for demonstration
    step_by_step_solution = [
        f"Step 1: Convert the number {number} from base {from_base} to base 10:",
        f"        {number} (base {from_base}) = {base_10_value} (base 10).",
        f"Step 2: Convert the base 10 number to base {to_base}:",
        f"        {base_10_value} (base 10) = {correct_answer} (base {to_base}).",
        f"Step 3: The correct answer is {correct_answer}."
    ]
    
    return {
        "question": question,
        "options": options,
        "correct_answer": correct_answer,
        "explanation": explanation,
        "step_by_step_solution": step_by_step_solution
    }