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# modules/conversion_bases.py
title = "Conversion Between Bases"
description = "This module covers conversion techniques between different bases, including with and without fractions."
def generate_question():
import random
# Choose a base and corresponding valid digits
from_base = random.choice([2, 8, 10, 16])
to_base = random.choice([2, 8, 10, 16])
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
base_10 = int(number, from_base)
# Convert from base 10 to `to_base`
if to_base == 10:
return str(base_10)
elif to_base == 16:
return hex(base_10)[2:].upper()
elif to_base == 8:
return oct(base_10)[2:]
elif to_base == 2:
return bin(base_10)[2:]
correct_answer = 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 != correct_answer:
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 = [
f"Step 1: Convert the number {number} from base {from_base} to base 10.",
f"Step 2: Convert the base 10 number to 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
}
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