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import random |
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title = "2's Complement" |
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description = "This module covers the representation of numbers using the 2's complement method, which is commonly used for representing negative numbers in binary." |
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def generate_question(): |
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num = random.randint(-8, 7) |
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bit_length = 4 |
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if num >= 0: |
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binary = bin(num)[2:].zfill(bit_length) |
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else: |
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binary = bin((1 << bit_length) + num)[2:] |
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question = f"What is the 2's complement representation of {num}?" |
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correct_answer = binary |
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options = [correct_answer] |
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while len(options) < 5: |
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fake_option = bin(random.randint(-8, 7) & 0xF)[2:] |
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if fake_option not in options: |
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options.append(fake_option) |
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random.shuffle(options) |
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explanation = ( |
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f"The 2's complement representation of {num} is {binary}." |
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"\n\n**Step-by-step solution:**\n" |
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"1. If the number is positive, convert it to binary and pad with leading zeros to fit the bit length.\n" |
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"2. If the number is negative, take its absolute value, convert to binary, invert the digits, and add 1.\n" |
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"3. The result is the 2's complement representation." |
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) |
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return question, options, correct_answer, explanation |
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