An$($m$,$n$)$correlatingbranchpredictoruses thebehaviorof themost

recentmexecutedbranchestochoosefrom$2$mpredictors,eachofwhichisann

bitpredictor.Atwo$-$levellocalpredictorworksinasimilarfashion,butonlykeeps

trackofthepastbehaviorofeachindividualbranchtopredictfuturebehavior.

Thereisadesigntrade$-$off involvedwithsuchpredictors:correlatingpredictors

requirelittlememoryforhistory,whichallowsthemtomaintain$2-$bitpredictors

for a largenumber of individual branches $($reducing theprobabilityof branch

instructions reusingthesamepredictor$),$while localpredictors requiresubstan

tiallymorememorytokeephistoryandarethus limitedtotrackingarelatively

smallnumberofbranchinstructions.Forthisexercise,considera$(1,2)$correlating

predictorthatcantrackfourbranches$($requiring$16$bits$)$versusa$(1,2)$localpre

dictorthatcantracktwobranchesusingthesameamountofmemory.Forthefol

lowingbranchoutcomes,provideeachprediction,thetableentryusedtomakethe

prediction,anyupdatestothetableasaresultoftheprediction,andthefinalmis

predictionrateofeachpredictor.Assumethatallbranchesuptothispointhave

beentaken. Initializeeachpredictor tothefollowing