▁times . ▁ ▁Because ▁two ▁is ▁the ▁base ▁of ▁the ▁binary ▁numer al ▁system , ▁powers ▁of ▁two ▁are ▁common ▁in ▁computer ▁science . ▁Writ ten ▁in ▁binary , ▁a ▁power ▁of ▁two ▁always ▁has ▁the ▁form ▁ 1 0 0 … 0 0 0 ▁or ▁ 0 . 0 0 … 0 0 1 , ▁just ▁like ▁a ▁power ▁of ▁ten ▁in ▁the ▁decimal ▁system . ▁ ▁Computer ▁science ▁ ▁Two ▁to ▁the ▁power ▁of ▁, ▁written ▁as ▁, ▁is ▁the ▁number ▁of ▁ways ▁the ▁bits ▁in ▁a ▁binary ▁word ▁of ▁length ▁ ▁can ▁be ▁arranged . ▁A ▁word , ▁interpreted ▁as ▁an ▁unsigned ▁integer , ▁can ▁represent ▁values ▁from ▁ 0   () ▁to ▁  () ▁inclus ively . ▁Cor respond ing ▁signed ▁integer ▁values ▁can ▁be ▁positive , ▁negative ▁and ▁zero ; ▁see ▁signed ▁number ▁representations . ▁Either ▁way , ▁one ▁less ▁than ▁a ▁power ▁of ▁two ▁is ▁often ▁the ▁upper ▁bound ▁of ▁an ▁integer ▁in ▁binary ▁computers . ▁As ▁a ▁consequence , ▁numbers ▁of ▁this ▁form ▁show ▁up ▁frequently ▁in ▁computer ▁software . ▁As ▁an ▁example , ▁a ▁video ▁game ▁running ▁on ▁an ▁ 8 - bit ▁system ▁might ▁limit ▁the ▁score ▁or ▁the ▁number ▁of ▁items ▁the ▁player ▁can ▁hold ▁to ▁ 2 5 5 — the ▁result ▁of ▁using ▁a ▁byte , ▁which ▁is ▁ 8 ▁bits ▁long , ▁to ▁store ▁the ▁number , ▁giving ▁a ▁maximum ▁value ▁of ▁. ▁ ▁For ▁example , ▁in ▁the ▁original ▁Leg end ▁of ▁Zel da ▁the ▁main ▁character ▁was ▁limited