Exam-style question
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A negative floating point value has the unnormalised form -0.001101 × 2^7. Normalise it and explain the effect on the exponent.
Model answer
What a good answer should say
- -0.1101 × 2^4
Explanation
Why this works
Move the binary point three places to the right, changing the mantissa from -0.001101 to -0.1101. This makes the magnitude of the mantissa 2^3 times larger, so the exponent must decrease by 3, from 7 to 4.
The value is unchanged because the increase in the mantissa is balanced by the decrease in the exponent. The resulting negative mantissa is in normalised form.
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