Exam-style question
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A system has enough bits to store the binary fraction 0.101 exactly. Explain what this tells you about the stored value, and contrast it with storing the decimal value 0.110.
Model answer
What a good answer should say
- The binary fraction 0.101 can be stored exactly if the system has the required number of bits, so reading it back gives the same value represented by that binary fraction.
- In contrast, the decimal value 0.110 cannot be represented exactly by a finite binary fraction.
- Even if the system uses enough bits for a particular storage format, the representation of 0.110 must remain an approximation, so a rounding error can occur.
Explanation
Why this works
The answer distinguishes a value that is already a finite binary fraction from a decimal value that cannot ever be represented exactly by a finite binary fraction. The number of available bits matters for 0.101, while no finite increase in bits makes 0.110 exact in binary.
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