Answer to Question #151618 in Assembler for Raziya

Question

In 8087 math co-processors, what is the bias for a double precision floating point
representation? Demonstrate the conversion of a 64 bit floating point number into
corresponding decimal value.

Answer 1

The bias for a double precision floating point representation = 1023

The general representation formula is:

(-1)^s * (1+mantissa) * 2^(Exponent – 1023)

An invisible leading bit (i.e. it is not actually stored) with value 1.0 is placed in front, then bit 51 has a value of 1/2, bit 50 has value 1/4 etc. As a result, the mantissa has a value between 1.0 and 2

Sign

bit   Exponent                        Mantissa

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63 62                  52   51                                                                                                                          0

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 1  100 0000 0010    1110 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000

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 (-1)^1        2^3                     1 + 1/2 + 1/4 + 1/8

-1 * 8 * 1.875 =-15