▁any ▁stage ▁shall ▁be ▁independent ▁of ▁its ▁on / off ▁switch ▁position , ▁and ▁must ▁be ▁equal ▁to ▁R source . ▁ ▁This ▁leads ▁to : ▁ ▁Again , ▁all ▁res istor ▁values ▁of ▁the ▁circuit ▁diagram ▁follow ▁easily ▁after ▁choosing ▁values ▁for ▁N , ▁ ▁and ▁R source . ▁( The ▁value ▁of ▁R load ▁does ▁not ▁influence ▁the ▁log arith mic ▁behavior ) ▁ ▁Circ uit ▁variations ▁▁ ▁The ▁circuit ▁as ▁dep icted ▁above , ▁can ▁also ▁be ▁applied ▁in ▁reverse ▁direction . ▁That ▁corresponding ly ▁revers es ▁the ▁role ▁of ▁constant - input ▁and ▁constant - output ▁resistance ▁equations . ▁ ▁Since ▁the ▁stages ▁do ▁not ▁influence ▁each ▁other ' s ▁at ten u ation , ▁the ▁stage ▁order ▁can ▁be ▁chosen ▁arbitr arily . ▁Such ▁re order ing ▁can ▁have ▁a ▁significant ▁effect ▁on ▁the ▁input ▁resistance ▁of ▁the ▁constant ▁output ▁resistance ▁at ten u ator ▁and ▁vice ▁vers a . ▁ ▁Background ▁ ▁R - 2 R ▁lad der ▁networks ▁used ▁for ▁Digital - to - Anal og ▁conversion ▁are ▁rather ▁old . ▁A ▁historic ▁description ▁is ▁in ▁a ▁pat ent ▁file d ▁in ▁ 1 9 5 5 . ▁ ▁Mult ip lying ▁DA - con ver ters ▁with ▁log arith mic ▁behavior ▁were ▁not ▁known ▁for ▁a ▁long ▁time ▁after ▁that . ▁An ▁initial ▁approach ▁was ▁to ▁map ▁the ▁log arith mic ▁code ▁to ▁a ▁much ▁longer ▁code ▁word , ▁which ▁could ▁be ▁applied ▁to ▁the ▁classical ▁( linear ) ▁R - 2 R ▁based ▁DA