$n = unpack 'N', pack 'B32', '01000010001111000000000000000000';;

( $s, $c, $e ) = ( 
    $n & 0x8000_0000, 
    (( $n >> 24 ) & 0x7f) - 64, 
    (($n & 0x00ffffff) / 0xffffff) * 16 
);;

print $s, $c, $e;;
0 2 3.75000022351743

$num = ($s? -1 : 1 ) * $e * 10**$c;;

print $num;;