Для перевода шестнадцатеричного числа FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF в десятичное необходимо записать его в виде многочлена, состоящего из произведений цифр вида:
A16 = an-1 ∙ 16n-1 + an-2 ∙ 16n-2 + ∙∙∙ + a0 ∙ 160
В результате преобразований получим:
FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF16=F ∙ 16113 + F ∙ 16112 + F ∙ 16111 + F ∙ 16110 + F ∙ 16109 + F ∙ 16108 + F ∙ 16107 + F ∙ 16106 + F ∙ 16105 + F ∙ 16104 + F ∙ 16103 + F ∙ 16102 + F ∙ 16101 + F ∙ 16100 + F ∙ 1699 + F ∙ 1698 + F ∙ 1697 + F ∙ 1696 + F ∙ 1695 + F ∙ 1694 + F ∙ 1693 + F ∙ 1692 + F ∙ 1691 + F ∙ 1690 + F ∙ 1689 + F ∙ 1688 + F ∙ 1687 + F ∙ 1686 + F ∙ 1685 + F ∙ 1684 + F ∙ 1683 + F ∙ 1682 + F ∙ 1681 + F ∙ 1680 + F ∙ 1679 + F ∙ 1678 + F ∙ 1677 + F ∙ 1676 + F ∙ 1675 + F ∙ 1674 + F ∙ 1673 + F ∙ 1672 + F ∙ 1671 + F ∙ 1670 + F ∙ 1669 + F ∙ 1668 + F ∙ 1667 + F ∙ 1666 + F ∙ 1665 + F ∙ 1664 + F ∙ 1663 + F ∙ 1662 + F ∙ 1661 + F ∙ 1660 + F ∙ 1659 + F ∙ 1658 + F ∙ 1657 + F ∙ 1656 + F ∙ 1655 + F ∙ 1654 + F ∙ 1653 + F ∙ 1652 + F ∙ 1651 + F ∙ 1650 + F ∙ 1649 + F ∙ 1648 + F ∙ 1647 + F ∙ 1646 + F ∙ 1645 + F ∙ 1644 + F ∙ 1643 + F ∙ 1642 + F ∙ 1641 + F ∙ 1640 + F ∙ 1639 + F ∙ 1638 + F ∙ 1637 + F ∙ 1636 + F ∙ 1635 + F ∙ 1634 + F ∙ 1633 + F ∙ 1632 + F ∙ 1631 + F ∙ 1630 + F ∙ 1629 + F ∙ 1628 + F ∙ 1627 + F ∙ 1626 + F ∙ 1625 + F ∙ 1624 + F ∙ 1623 + F ∙ 1622 + F ∙ 1621 + F ∙ 1620 + F ∙ 1619 + F ∙ 1618 + F ∙ 1617 + F ∙ 1616 + F ∙ 1615 + F ∙ 1614 + F ∙ 1613 + F ∙ 1612 + F ∙ 1611 + F ∙ 1610 + F ∙ 169 + F ∙ 168 + F ∙ 167 + F ∙ 166 + F ∙ 165 + F ∙ 164 + F ∙ 163 + F ∙ 162 + F ∙ 161 + F ∙ 160 = 15 ∙ 1.162941958873E+136 + 15 ∙ 7.2683872429561E+134 + 15 ∙ 4.5427420268475E+133 + 15 ∙ 2.8392137667797E+132 + 15 ∙ 1.7745086042373E+131 + 15 ∙ 1.1090678776483E+130 + 15 ∙ 6.931674235302E+128 + 15 ∙ 4.3322963970638E+127 + 15 ∙ 2.7076852481649E+126 + 15 ∙ 1.692303280103E+125 + 15 ∙ 1.0576895500644E+124 + 15 ∙ 6.6105596879025E+122 + 15 ∙ 4.1315998049391E+121 + 15 ∙ 2.5822498780869E+120 + 15 ∙ 1.6139061738043E+119 + 15 ∙ 1.0086913586277E+118 + 15 ∙ 6.3043209914231E+116 + 15 ∙ 3.9402006196394E+115 + 15 ∙ 2.4626253872747E+114 + 15 ∙ 1.5391408670467E+113 + 15 ∙ 9.6196304190416E+111 + 15 ∙ 6.012269011901E+110 + 15 ∙ 3.7576681324381E+109 + 15 ∙ 2.3485425827738E+108 + 15 ∙ 1.4678391142336E+107 + 15 ∙ 9.1739944639603E+105 + 15 ∙ 5.7337465399752E+104 + 15 ∙ 3.5835915874845E+103 + 15 ∙ 2.2397447421778E+102 + 15 ∙ 1.3998404638611E+101 + 15 ∙ 8.749002899132E+99 + 15 ∙ 5.4681268119575E+98 + 15 ∙ 3.4175792574735E+97 + 15 ∙ 2.1359870359209E+96 + 15 ∙ 1.3349918974506E+95 + 15 ∙ 8.3436993590661E+93 + 15 ∙ 5.2148120994163E+92 + 15 ∙ 3.2592575621352E+91 + 15 ∙ 2.0370359763345E+90 + 15 ∙ 1.2731474852091E+89 + 15 ∙ 7.9571717825566E+87 + 15 ∙ 4.9732323640979E+86 + 15 ∙ 3.1082702275612E+85 + 15 ∙ 1.9426688922257E+84 + 15 ∙ 1.2141680576411E+83 + 15 ∙ 7.5885503602568E+81 + 15 ∙ 4.7428439751605E+80 + 15 ∙ 2.9642774844753E+79 + 15 ∙ 1.8526734277971E+78 + 15 ∙ 1.1579208923732E+77 + 15 ∙ 7.2370055773323E+75 + 15 ∙ 4.5231284858327E+74 + 15 ∙ 2.8269553036454E+73 + 15 ∙ 1.7668470647784E+72 + 15 ∙ 1.1042794154865E+71 + 15 ∙ 6.9017463467906E+69 + 15 ∙ 4.3135914667441E+68 + 15 ∙ 2.6959946667151E+67 + 15 ∙ 1.6849966666969E+66 + 15 ∙ 1.0531229166856E+65 + 15 ∙ 6.5820182292848E+63 + 15 ∙ 4.113761393303E+62 + 15 ∙ 2.5711008708144E+61 + 15 ∙ 1.606938044259E+60 + 15 ∙ 1.0043362776619E+59 + 15 ∙ 6.2771017353867E+57 + 15 ∙ 3.9231885846167E+56 + 15 ∙ 2.4519928653854E+55 + 15 ∙ 1.5324955408659E+54 + 15 ∙ 9.5780971304118E+52 + 15 ∙ 5.9863107065074E+51 + 15 ∙ 3.7414441915671E+50 + 15 ∙ 2.3384026197294E+49 + 15 ∙ 1.4615016373309E+48 + 15 ∙ 9.1343852333181E+46 + 15 ∙ 5.7089907708238E+45 + 15 ∙ 3.5681192317649E+44 + 15 ∙ 2.2300745198531E+43 + 15 ∙ 1.3937965749082E+42 + 15 ∙ 8.711228593176E+40 + 15 ∙ 5.444517870735E+39 + 15 ∙ 3.4028236692094E+38 + 15 ∙ 2.1267647932559E+37 + 15 ∙ 1.3292279957849E+36 + 15 ∙ 8.3076749736557E+34 + 15 ∙ 5.1922968585348E+33 + 15 ∙ 3.2451855365843E+32 + 15 ∙ 2.0282409603652E+31 + 15 ∙ 1.2676506002282E+30 + 15 ∙ 7.9228162514264E+28 + 15 ∙ 4.9517601571415E+27 + 15 ∙ 3.0948500982135E+26 + 15 ∙ 1.9342813113834E+25 + 15 ∙ 1.2089258196146E+24 + 15 ∙ 7.5557863725914E+22 + 15 ∙ 4.7223664828696E+21 + 15 ∙ 2.9514790517935E+20 + 15 ∙ 1.844674407371E+19 + 15 ∙ 1152921504606846976 + 15 ∙ 72057594037927936 + 15 ∙ 4503599627370496 + 15 ∙ 281474976710656 + 15 ∙ 17592186044416 + 15 ∙ 1099511627776 + 15 ∙ 68719476736 + 15 ∙ 4294967296 + 15 ∙ 268435456 + 15 ∙ 16777216 + 15 ∙ 1048576 + 15 ∙ 65536 + 15 ∙ 4096 + 15 ∙ 256 + 15 ∙ 16 + 15 ∙ 1 = 1.7444129383095E+137 + 1.0902580864434E+136 + 6.8141130402713E+134 + 4.2588206501696E+133 + 2.661762906356E+132 + 1.6636018164725E+131 + 1.0397511352953E+130 + 6.4984445955957E+128 + 4.0615278722473E+127 + 2.5384549201546E+126 + 1.5865343250966E+125 + 9.9158395318537E+123 + 6.1973997074086E+122 + 3.8733748171304E+121 + 2.4208592607065E+120 + 1.5130370379415E+119 + 9.4564814871347E+117 + 5.9103009294592E+116 + 3.693938080912E+115 + 2.30871130057E+114 + 1.4429445628562E+113 + 9.0184035178515E+111 + 5.6365021986572E+110 + 3.5228138741607E+109 + 2.2017586713505E+108 + 1.376099169594E+107 + 8.6006198099628E+105 + 5.3753873812267E+104 + 3.3596171132667E+103 + 2.0997606957917E+102 + 1.3123504348698E+101 + 8.2021902179363E+99 + 5.1263688862102E+98 + 3.2039805538814E+97 + 2.0024878461759E+96 + 1.2515549038599E+95 + 7.8222181491244E+93 + 4.8888863432028E+92 + 3.0555539645017E+91 + 1.9097212278136E+90 + 1.1935757673835E+89 + 7.4598485461468E+87 + 4.6624053413417E+86 + 2.9140033383386E+85 + 1.8212520864616E+84 + 1.1382825540385E+83 + 7.1142659627407E+81 + 4.4464162267129E+80 + 2.7790101416956E+79 + 1.7368813385597E+78 + 1.0855508365998E+77 + 6.784692728749E+75 + 4.2404329554681E+74 + 2.6502705971676E+73 + 1.6564191232297E+72 + 1.0352619520186E+71 + 6.4703872001162E+69 + 4.0439920000726E+68 + 2.5274950000454E+67 + 1.5796843750284E+66 + 9.8730273439272E+64 + 6.1706420899545E+63 + 3.8566513062216E+62 + 2.4104070663885E+61 + 1.5065044164928E+60 + 9.41565260308E+58 + 5.884782876925E+57 + 3.6779892980781E+56 + 2.2987433112988E+55 + 1.4367145695618E+54 + 8.9794660597611E+52 + 5.6121662873507E+51 + 3.5076039295942E+50 + 2.1922524559964E+49 + 1.3701577849977E+48 + 8.5634861562358E+46 + 5.3521788476473E+45 + 3.3451117797796E+44 + 2.0906948623622E+43 + 1.3066842889764E+42 + 8.1667768061025E+40 + 5.1042355038141E+39 + 3.1901471898838E+38 + 1.9938419936774E+37 + 1.2461512460484E+36 + 7.7884452878022E+34 + 4.8677783048764E+33 + 3.0423614405478E+32 + 1.9014759003423E+31 + 1.188422437714E+30 + 7.4276402357123E+28 + 4.6422751473202E+27 + 2.9014219670751E+26 + 1.8133887294219E+25 + 1.1333679558887E+24 + 7.0835497243045E+22 + 4.4272185776903E+21 + 2.7670116110564E+20 + 1.7293822569103E+19 + 1080863910568919040 + 67553994410557440 + 4222124650659840 + 263882790666240 + 16492674416640 + 1030792151040 + 64424509440 + 4026531840 + 251658240 + 15728640 + 983040 + 61440 + 3840 + 240 + 15 = 1.8607071341968E+13710
Таким образом:
FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF16 = 1.8607071341968E+13710.