my $f = unpack('N',  pack('B32', "01000010001111000000000000000000")) ;

printf "0x%08X = %12.9f\n", $f, conv_BFP($f) ;

sub conv_BFP {
  my ($f) = @_ ;

  my $s = ($f & 0x8000_0000) ? -1 : +1 ;
  my $e = ((($f >> 23) & 0xFF) - 0x7F) - 23 ;

  return $s * (($f & 0x7F_FFFF) | 0x80_0000) * (2 ** $e) ;
} ;