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 1.32487359893280124981233898124124 times 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.ddd,dd); (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 times 2^e, 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.

Explanation / Answer

First of all it will be converted to binary number and that is

0.0000000000000000000000000000000000000000000000000000000011110100011001010110001100000011110001110001

i.e, 1.1110100011001010110001100000011110001110001 * 2-57, now exponent's value is -57.

sign is positive and mantissa is 1110100011001010110001100000011110001110001.

now we can write

and in hexa decimal the number is

0x3C6E8CAC6078E200

Now, in order to write it in double precision floating point format we need to write this number in normalized form

So the answer will be

1) 132.487359893280127146769272484e-19

2) 111.1010001100101011000110000001111000111000100000000000000000000000000000000000000000000000000000000000000000

3) 1.1110100011001010110001100000011110001110001 *2-57

4) 1110100011001010110001100000011110001110001000000000

5) Biased exponent (in binary): 01111000110

   Biased exponent (in decimal): 966

6) 0011110001101110100011001010110001100000011110001110001000000000

7) 0x3C6E8CAC6078E200

If you like the answer, please give a thumbs up.Thanks

Sign Exponent
Mantissa 0
01111000110 1110100011001010110001100000011110001110001000000000

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