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IEEE 754 Single Precision

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Question 1 (a) Convert the positive decimal number 17.45 to IEEE 754 single precision representation. Show all of your working out. [15 marks]

(b) In IEEE 754 single precision, 1.25 is represented as: 0 01111111 01000000000000000000000

In IEEE 754 single precision 1.26 is represented as: 0 01111111 01000010100011110101110

Explain why there are many more 1’s in the mantissa of the IEEE 754 representation of 1.26 than 1.25. [10 marks]

(c) Why is the exponent biased in IEEE representation? [5 marks]

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