What would be the IEEE 754 double precision floating point representation of 1.3

Question

What would be the IEEE 754 double precision floating point representation of 1.3248735989328012498123 3898124124 × 10-17. For explanation, I want you to document the steps you perform, in this order: (1) What is n in decimal fixed point form (ddd.ddddd); (2) What is n in binary fixed point form (bbb.bbbb), storing the first 110 bits following the binary point); (3) What is the normalized binary number, written in the form 1.bbbbb...bbb × 2e , storing 54 bits following the binary point) (4) What are the 52 mantissa bits, after the bits in bit positions -53, -54, ... are eliminated using the round to nearest, ties to even mode; exclude the 1. part; (5) What is the biased exponent in decimal and in binary? (6) Write the 64-bits of the number in the order: s e m; and (7) Write the final answer as a 16- hexdigit number.

Please do it in order with a brief expanation for each point. I have a test coming up and the questions will likely be asked in this format.

Explanation / Answer

normalized binary number for the given number:

1.1110100011001010110001100000011110001110001x2-57

52 mantissa bits

64 bits: sign|exponent|mantissa

0 01111000110 1110100011001010110001100000011110001110001000000000

Hexa decimal constant

0x1.e8cac60782ep-57

HexaDecimalNumber (sign|exponent|mantissa)

3c6e86cac6078e200

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