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import random |
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title = "Grouping Techniques for Base Conversion" |
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description = "This module covers the techniques used for converting binary numbers to octal and hexadecimal by grouping bits." |
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def generate_question(): |
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binary_num = bin(random.randint(1, 63))[2:] |
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padded_binary = binary_num.zfill(len(binary_num) + (3 - len(binary_num) % 3) % 3) |
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octal = ''.join([str(int(padded_binary[i:i+3], 2)) for i in range(0, len(padded_binary), 3)]) |
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question = f"Group the binary number {binary_num} into octal." |
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correct_answer = octal |
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options = [correct_answer] |
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while len(options) < 5: |
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fake_option = ''.join([str(random.randint(0, 7)) for _ in range(len(octal))]) |
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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 binary number {binary_num} is grouped into octal as {octal}." |
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"\n\n**Step-by-step solution:**\n" |
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"1. Pad the binary number with leading zeros to make its length a multiple of 3.\n" |
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"2. Group the binary digits in groups of three, starting from the right.\n" |
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"3. Convert each group to its octal equivalent." |
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) |
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return question, options, correct_answer, explanation |
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