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 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.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 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- hex digit number.

Explanation / Answer

                     Sign       Exponent                   Mantissa

Value                +          256                           1.32487359893280124981233898124124

Encoded as       0          56+1023 = 1079       3776860365959512
    
Binary               0          10000110111             1101 01101011 00001000 11010100 01111010 10110001 01011000

The final IEEE 754 double precision floating representation is : (01000011 01111101 01101011 00001000 11010100 01111010 10110001 01011000)2

The final hexadecimal representation is 0x437D6B08D47AB158

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