| 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] |
| |
| |
| 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 |
| } |
|
|
