Exam-style question
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Normalise 0.001011 × 2^5. Show how the mantissa and exponent change, and explain why the numerical value is unchanged.
Model answer
What a good answer should say
- 0.1011 × 2^2
Explanation
Why this works
Move the binary point three places to the right: 0.001011 becomes 0.1011. Because the mantissa has been multiplied by 2^3, the exponent must be reduced by 3, changing 5 to 2.
Therefore, 0.001011 × 2^5 and 0.1011 × 2^2 have the same value. The new mantissa begins with 01 and is normalised for a positive mantissa.
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