Stax, 19 14 bytes

üâïc-Hò~÷]ó┬ó♪

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Stax, 19 14 bytes

üâïc-Hò~÷]ó┬ó♪

Run and debug it

Unpacked, ungolfed, and commented, the code looks like this.

|a      absolute value
{HcDw   double until there's no fractional part
@       convert to integer type
:B      convert to binary digits
D52(    drop the first digit, then pad to 52
:b      convert back number

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Stax, 19 bytes

«ö₧σ☼ZÜ▲.├£HD╝♥♀!T·

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Unpacked, ungolfed, and commented, the program looks like this.

|a          absolute value
{hc1>w      halve until <1
{Hc1<n*w    double until >1 OR =0
D52|2*      multiply fractional part by 2**52
@           output as integer

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Stax, 19 14 bytes

üâïc-Hò~÷]ó┬ó♪

Run and debug it