import random

title = "Subtraction in Bases"
description = "This module covers subtraction operations in various bases, such as binary, octal, decimal, and hexadecimal."

def generate_valid_number(base, length):
    if base == 16:
        return ''.join(random.choices('0123456789ABCDEF', k=length))
    elif base == 10:
        return ''.join(random.choices('0123456789', k=length))
    elif base == 8:
        return ''.join(random.choices('01234567', k=length))
    elif base == 2:
        return ''.join(random.choices('01', k=length))
    else:
        raise ValueError("Unsupported base")

def subtract_numbers(num1, num2, base):
    return bin(int(num1, base) - int(num2, base))[2:] if base == 2 else \
           oct(int(num1, base) - int(num2, base))[2:] if base == 8 else \
           str(int(num1, base) - int(num2, base)) if base == 10 else \
           hex(int(num1, base) - int(num2, base))[2:].upper()

def generate_question():
    base = random.choice([2, 8, 10, 16])
    length = random.randint(3, 5)
    
    num1 = generate_valid_number(base, length)
    num2 = generate_valid_number(base, length)
    
    correct_answer = subtract_numbers(num1, num2, base)
    options = [correct_answer]
    
    # Generate other random options
    while len(options) < 4:
        fake_answer = subtract_numbers(generate_valid_number(base, length), generate_valid_number(base, length), base)
        if fake_answer not in options:
            options.append(fake_answer)
    
    random.shuffle(options)
    
    question = f"What is the result of subtracting {num2} from {num1} in base {base}?"
    explanation = f"To subtract {num2} from {num1} in base {base}, convert both numbers to base 10, perform the subtraction, and convert the result back to base {base}."
    step_by_step_solution = [
        f"1. Convert {num1} and {num2} to base 10.",
        f"2. Subtract the base 10 equivalents.",
        f"3. Convert the result back to base {base}.",
        f"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
    }