▁of ▁the ▁circuit ▁is ▁its ▁main ▁differenti ator ▁in ▁comparison ▁with ▁digital - to - anal og ▁conver ters ▁in ▁general , ▁and ▁traditional ▁R - 2 R ▁Lad der ▁networks ▁specifically . ▁Log arith mic ▁at ten u ation ▁is ▁desired ▁in ▁situations ▁where ▁a ▁large ▁dynamic ▁range ▁needs ▁to ▁be ▁handled . ▁The ▁circuit ▁described ▁in ▁this ▁article ▁is ▁applied ▁in ▁audio ▁devices , ▁since ▁human ▁per ception ▁of ▁sound ▁level ▁is ▁properly ▁expressed ▁on ▁a ▁log arith mic ▁scale . ▁ ▁Log arith mic ▁input / output ▁behavior ▁ ▁As ▁in ▁digital - to - anal og ▁conver ters , ▁a ▁binary ▁word ▁is ▁applied ▁to ▁the ▁lad der ▁network , ▁whose ▁N ▁bits ▁are ▁treated ▁as ▁representing ▁an ▁integer ▁value ▁according ▁to ▁the ▁relation : ▁ ▁where ▁ ▁represents ▁a ▁value ▁ 0 ▁or ▁ 1 ▁depending ▁on ▁the ▁state ▁of ▁the ▁it h ▁switch . ▁ ▁For ▁a ▁conventional ▁D AC ▁or ▁R - 2 R ▁network , ▁the ▁output ▁signal ▁value ▁( its ▁voltage ) ▁would ▁be : ▁ ▁where ▁ ▁and ▁ ▁are ▁design ▁constants ▁and ▁where ▁ ▁typically ▁is ▁a ▁constant ▁reference ▁voltage . ▁( DA - con ver ters ▁that ▁are ▁designed ▁to ▁handle ▁a ▁variable ▁input ▁voltage ▁are ▁term ed ▁multip lying ▁D AC .) ▁ ▁In ▁contrast , ▁the ▁log arith mic ▁lad der ▁network ▁discussed ▁in ▁this ▁article ▁creates ▁a ▁behavior ▁as : ▁ ▁where ▁ ▁is ▁a ▁variable ▁input ▁signal . ▁ ▁Circ uit ▁implementation ▁▁ ▁This ▁example ▁circuit ▁is