▁integers ▁mod ulo ▁n ). ▁ ▁Pow ers ▁of ▁ 1 0 2 4 ▁▁▁ ▁The ▁first ▁few ▁powers ▁of ▁ 2 1 0 ▁are ▁slightly ▁larger ▁than ▁those ▁same ▁powers ▁of ▁ 1 0 0 0 : ▁ ▁Pow ers ▁of ▁two ▁whose ▁ex ponents ▁are ▁powers ▁of ▁two ▁ ▁Because ▁data ▁( specific ally ▁integers ) ▁and ▁the ▁addresses ▁of ▁data ▁are ▁stored ▁using ▁the ▁same ▁hardware , ▁and ▁the ▁data ▁is ▁stored ▁in ▁one ▁or ▁more ▁oct ets ▁( ), ▁double ▁expon entials ▁of ▁two ▁are ▁common . ▁For ▁example , ▁ ▁Several ▁of ▁these ▁numbers ▁represent ▁the ▁number ▁of ▁values ▁represent able ▁using ▁common ▁computer ▁data ▁types . ▁For ▁example , ▁a ▁ 3 2 - bit ▁word ▁consisting ▁of ▁ 4   bytes ▁can ▁represent ▁ ▁distinct ▁values , ▁which ▁can ▁either ▁be ▁regarded ▁as ▁mere ▁bit - pattern s , ▁or ▁are ▁more ▁commonly ▁interpreted ▁as ▁the ▁unsigned ▁numbers ▁from ▁ 0 ▁to ▁, ▁or ▁as ▁the ▁range ▁of ▁signed ▁numbers ▁between ▁ ▁and ▁. ▁Also ▁see ▁t etr ation ▁and ▁lower ▁hyper oper ations . ▁For ▁more ▁about ▁representing ▁signed ▁numbers ▁see ▁two ' s ▁complement . ▁ ▁In ▁a ▁connection ▁with ▁nim bers , ▁these ▁numbers ▁are ▁often ▁called ▁F erm at ▁ 2 - pow ers . ▁ ▁The ▁numbers ▁ ▁form ▁an ▁ir r ational ity ▁sequence : ▁for ▁every ▁sequence ▁ ▁of ▁positive ▁integers , ▁the ▁series ▁ ▁converges ▁to ▁an ▁ir r ational ▁number . ▁Despite ▁the ▁rapid ▁growth ▁of ▁this