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.

Explanation / Answer

Double-precision floating-point format is a computer number format that occupies 8 bytes (64 bits) in computer memory and represents a wide, dynamic range of values by using a floating point.

Double-precision floating-point format usually refers to binary64, as specified by the IEEE 754 standard, not to the 64-bit decimal formatdecimal64. In older computers, different floating-point formats of 8 bytes were used, e.g., GW-BASIC's double-precision data type was the 64-bit MBF floating-point format.

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