Exam-style question
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A system stores an unsigned binary value using 9 bits. State the minimum and maximum values it can store, then explain why these values are the limits.
Model answer
What a good answer should say
- The minimum value is 0 and the maximum value is 511.
- The minimum occurs when all 9 bits are 0.
- The maximum occurs when all 9 bits are 1, calculated as 2^9 - 1 = 512 - 1 = 511.
Explanation
Why this works
Unsigned binary represents non-negative values, so the all-zero pattern gives the minimum of 0. With 9 bits there are 2^9 possible patterns, ranging from 0 to one less than 2^9.
Therefore the maximum is 511.
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