IEEE 754 double precision binary floating point format

Express 0x5ABC8 in IEEE 754 double precision binary floating-point format.

First, converting 0x5ABC8 to binary:

0x5ABC8 =(101 1010101111001000 )2

Since, it a double precision (64 bits) then it will be:


Sign Exponent Mantissa
0000 00000000 00000000
0 00000000000 00000000 00000101 10101011 11001000

Since the exponent is 00000000000 and the mantissa is not identically zero, the
number is denormalized. Thus, the exponent is e min=−1022 and the hidden bit is
0. Therefore, it represents the number as shown in the table below:

IEEE 754 double precision binary floating point format
00000000 00000000 00000000 00000000
00000000 00000101 10101011 11001000
0x5ABC8
−1022
(0,0000000000000000000000 ¿000000000001011010101111001000)2 × 2 =¿