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If the 2 bits after the sign bit are "00", "01", or "10", then the exponent field consists of the 10 bits following the sign bit, and the significand is the remaining 53 bits, with an implicit leading 0 bit:
s 00 eeeeeeee [(0)ttttt][tttttttt][tttttttt][tttttttt][tttttttt][tttttttt][tttttttt]
s 01 eeeeeeee [(0)ttttt][tttttttt][tttttttt][tttttttt][tttttttt][tttttttt][tttttttt]
s 10 eeeeeeee [(0)ttttt][tttttttt][tttttttt][tttttttt][tttttttt][tttttttt][tttttttt]
This includes [[subnormal numbers]] where the leading significand digit is 0.
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