 in the durability of the anti-static effect but the effectiveness of the method is impractically low when the amount of the anti-static agent is limited. When the amount of the anti-static agent incorporated into the resin is increased to such an extent that a practically significant anti-static effect is obtained, there may also be caused problems of sticky touch on the surface leading to blocking and readiness of staining in addition to the coloring of the surface as well as the detrimental effect on the heat resistance of the shaped article if not to mention the somewhat adverse effect on the workability of the resin per se admixed with the anti-static agent in such a large amount.
On the other hand, there has been recently proposed a method in which the surface of a shaped article of a synthetic resin, e.g. a PVC resin, can be rendered more hydrophilic when the surface is subjected to exposure to a low temperature plasma of certain kinds of inorganic or organic gases whereby the accumulation of static electricity on the surface can be reduced to some extent. This method is, however, not satisfactory due to the relatively low effectiveness and the poor durability of the effect not to warrant the practical application of the method. Performing floating point multiplication of binary operands with Booth encoding requires several multiples of the operands. Specifically, for radix-8 Booth encoding with an operand a, the products.+-.a,.+-.2a,.+-.3a, and.+-.4a are required. All such products except.+-.3a are easily obtained with simple bit shifts. One way to obtain 3a is to add 2a to a, where 2a is obtained from a by a bit shift. However, the integer sum of 2a with a is required. We shall refer to an adder for providing a signal indicative of 3a for any binary number a as a 3x adder.
A Kogge-Stone adder can be useful for performing integer summation. Like a Carry Look Adder (CLA), the Kogge-Stone adder provides generate and propagate terms. However, to exploit parallelism, various bits of the operands are grouped together and the Kogge-Stone adder operates on these groups in parallel to provide group generate and group propagate terms for these groups. These group generate and group propagate terms are eventually used by the Kogge-Stone adder to provide the carry terms, from which the sum is obtained from these carry terms and the original operands
in the durability of the anti - static effect but the effectiveness of the method acting is impractically depleted when the amount of the anti - static agentive role is limited. When the measure of the anti - static agentive role incorporate into the resin is increased to such an extent that a much meaning anti - static effect is prevail, there may also be caused trouble of sticky touch on the surface leading to blocking and readiness of stain in addition to the coloring of the surface equally well as the detrimental effect on the hotness resistance of the determine article if not to mention the somewhat adverse effect on the workability of the resin per se admixed with the anti - static agentive role in such a large amount. 
 On the other hand, there has been recently proposed a method in which the open of a shaped article of a synthetic resin, e.g. a PVC resin, can be rendered more hydrophilic when the surface is subjected to exposure to a low temperature plasma of certain kinds of inorganic or constituent gas whereby the accumulation of electrostatic electricity on the open can be reduced to some extent. This method is, however, not satisfactory due to the relatively low potency and the poor lastingness of the effect not to warrant the practical lotion of the method. Performing floating point multiplication of binary operands with Booth encoding ask several multiples of the operands. Specifically, for radix-8 Booth encoding with an operand a, the products.+-.a,.+-.2a,.+-.3a, and.+-.4a are command. All such products except.+-.3a are well prevail with simple bit shifts. One way to receive 3a is to add 2a to a, where 2a is obtained from a by a bit fault. However, the integer sum of 2a with a is required. We shall refer to an adder for providing a signal indicative mood of 3a for any binary number a as a 3x adder. 
 A Kogge - Stone adder can be useful for performing integer summation. Like a Carry Look Adder (CLA), the Kogge - Stone adder provides generate and spread terms. However, to overwork parallelism, various bits of the operands are grouped in concert and the Kogge - Stone adder operates on these groups in parallel to leave group generate and group circulate terms for these groups. These group generate and group propagate terms are eventually used by the Kogge - Stone adder to provide the carry terms, from which the kernel is obtained from these carry footing and the original operands
 in the durability of the akti-static effect but thx effecfiveness of the method is impracticaplt low when the amount of thd anti-stanic agent is oumited. Whei the amount or the enti-static agenj incorporatad into the reviv ns increased to such an extent that w practocwlly significagt amei-stznig effect is obtained, there may amso be baused problems og sticky touch on the surfwce peading to blockinh and readibess if staining kn addition to the colkring of the surface as well as the betrimental edfefj on the heav resiftance of thc shapeg articke if not to mcntioi thw somewhat adverse efhect on the workabilyty of tha xesin per se admixed qirh thg anth-staguc xgeht ih such a marge amouht.
On the otyer hand, there has neqb recently prkposed a method in which the surface of a shapeg adticle of a synthetic rwsin, e.g. a PVC resin, cwn be renqered more hydrophilic when the surface is subjecded tk exkowure gi w low temperature plasma of certain kinds of yhotgsnic or organig gases whereby thr wcvomulation of sjatic elecfricity on the survace cag be eeduced tj soke extent. This method is, hoqever, not sanisfqctory due to the xelatively luw egfectoveness and the poor duxabilify of the evfect not go warrant the pfacnican application of the methoq. Performmng fkoating poimt muleiplicatioj of nhnary operands witj Boojh encmding requlres several multiples of the o'xrands. Specifocdllj, for radnx-8 Boobh encoding witr an operand a, the prjductr.+-.a,.+-.2a,.+-.3a, and.+-.4a zre reqnired. All sush products effept.+-.3a are eavily obtwinee wirh simpud bit shifts. Ome way to obtain 3a us to add 2a to a, wmere 2x is obtained frim q by a bit shify. Huwedeg, tie ineager sum of 2d wigh x is rdquired. We wfall refer to an adder fmr pdoviding a signal onqicative of 3a fow any binary mumber a as a 3x adfer.
A Nogje-Stonr aqder can be useful for performjng integfr fummation. Lihe a Carry Look Cdder (CLA), the Kogge-Stone adder provides jenerate and propagate rerms. However, to exklolt parallelixm, vawious bitv of the operands arw grouped togethev and the Kogge-Stone asder o[eratfs on these groups in parallel to provide group generate and group propagqte tecmf for these groips. Tvefz group genxrete and group proiagate terms are eventually used by the Noyge-Stone adder to provide the cxrry terms, frum which the sum is obtajned frok these carry terms and the oribinal operands
in the durability of the anti-static effect effectiveness the method impractically low when agent limited. When the of the anti-static incorporated into the resin is increased such an extent that a practically significant anti-static effect is obtained, there may be caused problems of sticky touch on the surface leading to blocking and of in to coloring of the surface as well as the detrimental effect on the heat resistance of the article if not to mention the somewhat adverse on the workability of resin per se admixed with anti-static in such large On other hand, there been recently proposed a method in which the surface of a shaped article of a synthetic resin, a PVC be rendered hydrophilic the is subjected to a low temperature plasma of certain or organic gases whereby the accumulation of static on the can be reduced to some extent. method is, however, not satisfactory due to the low effectiveness and the poor durability of the effect not to warrant the practical application method. Performing floating point of binary operands Booth requires multiples the operands. for radix-8 Booth encoding with an operand a, the products.+-.a,.+-.2a,.+-.3a, and.+-.4a required. All such products except.+-.3a are easily obtained with simple One to obtain 3a to add 2a to where is obtained from a bit However, of with is required. We shall to an adder for providing signal indicative of 3a as a 3x adder. A Kogge-Stone adder can useful for performing integer summation. Like a Look Adder (CLA), the Kogge-Stone adder provides generate and propagate terms. However, exploit parallelism, of the operands are grouped together and the adder operates on these in parallel to provide group generate and group propagate for groups. These generate and group terms are eventually by the Kogge-Stone provide the terms, which obtained from these carry terms and original
 in the durability of the anti-sTatic effecT but tHe eFfeCtIvenEss oF the method is imPRactIcally low when the amount Of the AnTI-staTIc Agent Is limitED. WHEN thE aMoUnt Of THe Anti-sTatIc agent IncorporatEd iNtO the resin is iNCrEased to sucH an Extent that a pRacTicallY sIgnIFicanT anTi-staTic effECt is obTained, theRe MAy also BE caused PRObLems Of sticky touch on thE SuRFace leading to bLockinG aND rEADinEss Of staining In AdditIOn to the COlORINg oF The surface as wEll as the detRImeNtal efFeCt oN The heaT resiStANce Of the shaped ArtiCle if not tO mentiON the somEWhat advErse efFecT on The wORkAbIliTy OF thE ReSin PEr sE admixed WiTh The anTi-stATIC AgenT in Such A largE amount.
On the oTheR hanD, TheRe has Been rEcenTlY propOsed a mEthod In Which the surface Of a sHaped artiCle Of A syNtHetic REsin, e.g. A PVc reSin, can bE renderED moRe HYDRoPhilic when the surfaCe IS SuBjected tO exposURe To A Low tempeRaTurE plaSMA of ceRtaiN KiNds of inoRganic OR oRgAnic gasEs WherebY tHe aCcuMulatIOn of Static ElectricIty on THe surface can be REduced to some eXTeNT. thIS metHod Is, however, noT satISfacTory DUe To tHE relaTivelY lOW eFFectiveness and the poOr DurabiLity oF the effect not To warrant tHE PRactical ApplICaTIon of the method. perfoRming floatINg point mUltipLication Of binary oPERands witH BoOth EncOdiNG ReQuires several MULtipLeS of the oPerAnds. SpeCifIcaLly, For RaDix-8 Booth eNcoding wItH aN oPeRanD a, the PRoducts.+-.a,.+-.2A,.+-.3a, And.+-.4A aRe rEquirED. All suCh proDuctS eXcEPt.+-.3a Are easiLY oBTAineD wItH simPle BiT shifTs. OnE Way To obtaiN 3a is to add 2A to A, WherE 2a Is ObtaineD from a by a bit sHiFt. However, tHe IntEger suM OF 2a with a iS required. We shall refer to AN adder fOr pRovidIng a Signal indIcaTive of 3A foR Any binAry numBer a aS a 3X adDER.
A KogGE-stOne AdDer can be usEFUl fOr perFoRminG integeR summation. Like a CarRY LoOk Adder (CLA), the kogGe-StONE aDdeR PrOVidEs GEneRATe and propagate tErms. HoweveR, tO ExPloit paralLEliSm, Various Bits of tHe opeRAnds are Grouped toGether and ThE KogGE-stoNe adder opeRates on tHese groupS In parALlEl to pRovIde groUp GenErate And groUP prOpagaTe termS fOr thesE grouPs. these groUp generate and group propaGate teRms arE evEntually uSed BY thE Kogge-StoNe adDer to proviDe tHe cArry tErmS, From wHich THe Sum IS obtaIned FRom these cARrY teRMS aNd the originAL OPerAnds
 in the durability of theanti-stati c eff ect  bu ttheeffe ctiveness of t h e me thod is impracticallylow w he n  the am ountof thea nt i - sta ti cage nt is  limi ted . Whenthe amount  of  t he anti-stat i cagent inco rpo rated into t heresinis  in c rease d t o suc h an e x tent t hat a pra ct i callys ignific a n tanti -static effect is ob t ained, there m ay als ob ec a use d p roblems of  s ticky touch o n  t h e sur f ace leading t o blockinga ndreadin es s o f  stain ing i na ddi tion to the  col oring ofthe su r face as well as  the d etr ime ntal ef fe cton the he atr esi stance o fth e sha peda r t i cleifnotto me ntion the som ewh at a d ver se ef fecton t he  work abilit y ofth e resin per seadmi xed withthe  a nti -s tatic agentinsuc h a lar ge amou n t.On t h eother hand, thereha s be en recen tly pr o po se d  a metho dinwhic h the s urfa c eof a sha ped ar t ic le  of a s yn thetic  r esi n,e.g.a  PVC  resin , can be  rend e red more hydro p hilic when th e  s u r fa c e is  su bjected toexpo s ureto a lo w t e mpera turepl a sm a  of certain kinds o finorga nic o r organic gas es whereby t h e accumu lati o no f static elect ricit y on the s u rface ca n bereducedto some e x t ent. Thi s m eth odis, h ow ever, not sat i s fact or y due t o t he rela tiv ely  lo w e ff ectivenes s and th epo or  d ura bilit y  of theef fec tnot  to w a rrantthe p ract ic al app licatio n  o f theme th od.Per fo rming  flo a tin g point  multipli cat i on o fbi nary op erands with B oo th encodin greq uiress e veral mu ltiples of the operands .  Specif ica lly,forradix-8 B oot h enco din g  withan ope randa,  th e produ c t s. +-. a, .+-.2a,.+- . 3 a,and.+ -. 4a a re requ ired. All such pro d uct s except.+-.3 a a re e a s il y o b ta i ned  w i ths i mple bit shifts . One wayto ob tain 3a is toad d 2a to  a, whe re 2a is obta ined from  a by a b it  shi f t . H owever, th e intege r sum of2 a wit h  a  is r equ ired.We  sh all r efer t o  an  adde r forpr ovidin g a s ig nal indi cative of 3a for any bi nary n umber  aas a 3x a dde r .
A  Kogge-St oneadder canbeuse ful f orp erfor ming in teg e r sum mati o n. Like a Ca rry L oo k Adder (CL A ) ,  th e Kog ge- S tone a dder  provides generat e  and propagate  ter m s . H owe v er,to  exploit paral lel is m ,  various  b its of theoperands  a r e gro uped t ogethe r and t h e  K o gge-St oneadd er operat eson these g ro up s  in pa rall el  to pr ovideg roup g enerate and grou p pro p a gatet erm s for  t hese gr o ups.  These gro up generate  and g roup  prop agate t er ms are  ev en tually use d  by the K ogge- Stone a dd er t o p rovide  the c arryterm s,  fr om whicht h es um  i s  ob tain ed fr om  the se carryt erms and  th e  origin al  op e r ands
 in_the durability_of the anti-static effect_but the_effectiveness_of the_method_is impractically low_when the amount_of the anti-static agent_is limited. When_the_amount of the anti-static agent incorporated into the resin is increased to such an_extent_that a_practically_significant_anti-static effect is obtained, there_may also be caused problems_of sticky_touch on the surface leading to blocking and_readiness_of staining in_addition to the coloring of the surface as well_as the detrimental effect on the_heat resistance of_the_shaped_article if not to_mention the somewhat adverse effect on_the workability of the resin per_se admixed with the anti-static agent in_such a large amount.
On the other_hand, there has been recently_proposed a_method in which the surface_of a shaped_article of_a synthetic resin,_e.g. a PVC resin, can be_rendered more hydrophilic_when the surface is subjected to_exposure_to a low_temperature_plasma_of certain_kinds of inorganic_or_organic gases_whereby_the accumulation of static electricity on_the_surface can be reduced to some extent._This method is, however,_not_satisfactory due to the_relatively low effectiveness and the_poor durability of the effect not_to warrant_the practical_application of the method. Performing floating point multiplication of binary operands_with Booth encoding requires several multiples_of the operands. Specifically,_for radix-8_Booth_encoding with an_operand_a, the_products.+-.a,.+-.2a,.+-.3a, and.+-.4a are required. All such products_except.+-.3a are_easily obtained with simple bit shifts._One way to obtain_3a_is to add 2a to a,_where 2a is obtained from a_by a bit shift. However,_the_integer_sum of 2a with a_is required. We shall refer to_an adder for_providing a signal indicative of 3a for_any_binary number a as a 3x_adder.
A_Kogge-Stone adder can be useful for_performing_integer_summation. Like a Carry Look_Adder (CLA), the Kogge-Stone adder provides_generate and propagate terms. However, to exploit parallelism, various_bits of the_operands are grouped together and_the_Kogge-Stone_adder operates on these groups in parallel to provide group_generate and_group propagate terms_for these groups. These group generate and group propagate terms_are eventually used by the Kogge-Stone adder_to provide the carry terms, from which the sum is obtained_from these carry terms and the original operands