Chapter 2 Literature Review


 Julius Richard
 4 years ago
 Views:
Transcription
1 Chpter 2 Literture Review 2.1 ADDER TOPOLOGIES Mny different dder rchitectures hve een proposed for inry ddition since 1950 s to improve vrious spects of speed, re nd power. Ripple Crry Adder hve the simplest rchitecture, ut performs slower ddition due to its longest crry propgtion dely (R.Um et l (2012)). Crry Sve Adder improves the speed of ddition y using N dditionl hlf dders in Ripple Crry Adder to reduce long crry propgtion dely, ut it consumes more re nd power thn Ripple Crry Adder (Chki Aloui (2011)). A crrylookhed dder performs fst ddition y reducing the mount of time required to determine crry its (YuTing Pi nd YuKumg Chen (2004)). It finds the crry it in dvnce for ech it position, whether tht position is going to propgte crry if 1 comes from the nerest LSB. On the other hnd, Crry Skip Adder nd Crry Select Adder speeding up the ddition where in the dders re split in locks of N its. In Crry Skip Adder, ech lock clcultes the crry it to propgte to the next lock sed on MSB crryout, ech it sum out nd LSB crryin (Yu Png et l (2012)). So tht the next lock towrds MSB need not to wit till the previous lock completes the ddition. The Crry Select Adder performs prllel ddition with crryin for 0 nd crryin for 1 (Sudhnshu Shekhr et l (2013)). Ech lock of dders generte finl sum with only multiplexer dely. So the Crry Select Adder performs fster thn ll other dders RIPPLE CARRY ADDER (RCA) The RCA is constructed y cscding series of full dder s s shown in Figure 2.1. The crryout of ech full dder is directly fed to the crryin of the next full dder. Ech full dder dding three digits nd generte crry it to the next full dder to strt computtion. Until the crry it is received from the previous dder, the next dder would not strt its computtion. This cuses the longest dely in RCA nd it increses linerly with the it size. 4
2 The dely of the RCA defined s, t = O(N) (2.1) where N is the opernd size in its. Even though RCA consumes more dely, due to its regulr structure, it tkes lesser re nd consumes lesser power. This mkes RCA s est choice to use in the low power pplictions. An Eqully Shred Block Scheme (ESBS) sed 16it RCA is shown in Figure 2.1. C16 4 it lock C12 4 it lock C8 4 it lock C C0 Ripple Crry Stges Figure 2.1: Schemtic of 16it RCA(CCrry it) CARRY SAVE ADDER (CSA) A 16it CSA structure is shown in Figure 2.2. It consists of N+1 hlf dders in the first stge nd N1 full dders in second stge. In the first stge, unlike sequentil 3it ddition in RCA, here two Nit ddition hppens in prllel to generte prtil sum. The prtil sum vlues re stored in the second stge full dders. The finl sum is then computed y shifting the crry sequence from LSB to MSB through the prtil sum vlues. 5
3 The dely of the CSA defined s, t = O(log N) (2.2) Even though CSA performs fster thn RCA, it increses re nd power due to its N dditionl hlf dder s. Since CSA hs regulr connectivity to propgte sum & crry to next stge, it is mostly used in multiplier designs to propgte the prtil sum nd prtil crry from ech stge H H H H H H H H H H H H H H H F Cin H F F F F F F F F F F F F F F H c15 c14 c13 c12 c11 c10 c9 c8 c7 c6 c5 c4 c3 c2 c1 s17 s16 s15 s14 s13 s12 s11 s10 s9 s8 s7 s6 s5 s4 s3 s2 s1 s0 Figure 2.2: Schemtic of 16it CSA (HHlf Adder, FFull Adder) CARRY LOOKAHEAD ADDER (CLA) A 4it CLA structure is shown in Figure 2.3. It speeds up the ddition y reducing the mount of time required to determine crry its. It uses two locks, crry genertor (Gi) nd crry propgtor (Pi) which finds the crry it in dvnce for ech it position from the nerest LSB, if the crry is 1 then tht position is going to propgte crry to next dder. 6
4 The generte lock cn e relized using the expression Gi = Ai. Bi for i=0,1,2,3 (2.3) Similrly the propgte lock cn e relized using the expression Pi = Ai Bi for i=0,1,2,3 (2.4) The crry output of the (i1) th stge is otined from Ci = Gi +Pi C i1 for i=0,1,2,3 (2.5) The sum output cn e otined using Si = Ai BiC i1 for i=0,1,2,3 (2.6) A 3 B 3 A 2 B 2 A 1 B 1 A 0 B 0 1 itfa 1 itfa 1 itfa 1 itfa C 0 S 3 S 2 S 1 S 0 C 4 P 3 G 3 C 3 P 2 G 2 C 2 P 1 G 1 C 1 P 0 G 0 4it Crry LookAhed Logic PG CG Figure 2.3: Schemtic of 4it CLA Even though the CLA is fster thn RCA, it increses re nd power due to its crry genertor nd propgtor logic. 7
5 2.1.4 CARRY SKIP ADDER (CSKA) A CSKA performs fst ddition since dders re split in locks of N its. It gretly reduces the dely of the dder through its criticl pth, since the crry it for ech lock cn e ypssed (skip) over the locks. It consists of simple RCA with ANDOR skip logic s shown in Figure 2.4. It genertes crryout from ech lock depending on MSB full dder crryout, LSB full dder crryin nd sum it of ech full dder. If the ANDOR skip logic output is 1, the current lock will e ypssed nd next lock will strt computtion. The dely of the CSKA defined s; t = (O( N) (2.7) The dditionl skip logic consumes slight re overhed in the CSKA, ut it is lesser thn CSA nd CLA. The design schemtic of 16it CSKA is shown in Figure it lock C12 4 it lock C8 4 it lock C C0 P[15,12] P[11,8] P[7,4] P[3,0] C16 Skip Logic Skip Logic Skip Logic Skip Logic(2 Gtes) Figure 2.4: Schemtic of 16it CSKA 8
6 2.1.5 CARRY SELECT ADDER (CSLA) A CSLA generlly consists of two RCA nd Multiplexer (Mux). It performs two dditions in prllel, y ssuming crryin of 0 nd crryin of 1. A CSLA performs fst ddition since dders re split in locks of N its A Kit CSLA is shown in Fig.2.5. It contins two groups of dders s one for lower N/2 its nd nother for higher N/2 its. The higher N/2 its group dder computes the prtil sum nd prtil crry y ssuming crryin 1 nd crryin 0 in prllel with the lower N/2 its. It genertes finl sum nd crry sed on the Mux selection input. Hence the dely of the CSLA cn e defined s, T selectdd (N) = T dd (N/2) + 1 (2.8) The CSLA is widely used in High performnce pplictions. But it consumes lrge re nd power due to its incresed hrdwre resources. Mny reserch rticles hve proposed vrious hints to reduce re nd power in the CSLA structure. N 1 N/2 k/2 N/2it RCA 0 N/2 1 0 N/2it k/2 it RCA 1 N/2it k/2 it RCA Cin N/2 + 1 N/2 + 1 k/ Mux Cout, Higher N/2 its Lower N/2 its Figure 2.5: Schemtic of Kit CSLA 9
7 2.1.6 OTHER ADDERS Kogge Stone dder is prllel prefix form crry lookhed dder (Kogge P nd Stone H (1973)). It hs regulr lyout nd minimum logic depth (fnout) which mkes fst dder ut hs lrge re. The dely of Kogge Stone dder is equl to log 2 N nd hs the re (N*log 2 N)N+1, where N is the numer of input its (N Zmhri et l (2012)). Another prllel prefix dder is Brent Kung Adder (R. P Brent nd H. T. Kung (1982)). It hs more logic depth (fnout) with minimum re chrcteristics. So it reduces its ddition speed, ut power efficient (N Zmhri et l (2012)). The dely of Brent Kung Adder is equl to (2*log 2 N)2 nd hs the re of (2N)2log 2 N. Ldner Fischer dder is nother prllel prefix dder (R.E. Ldner nd M.J. Fischer (1980)). Its dely nd re re symptoticlly optiml (i.e., logrithmic dely nd liner re). It hs n dditionl type of recursive step for constructing prllel prefix circuit. This dditionl recursive step reduces the dely, ut increses re. It hs dely of O(log N) nd re of O(N). An improvement tht cn e mde to CLA design is the use of pseudocrry s proposed y Ling, nd is clled Ling dder (H. Ling (1981)). This method llows single locl propgte signl to e removed from the criticl pth. HnCrlson dder is hyrid design tht mix of KoggeStone nd BrentKung dder (T. Hn nd D. Crlson (1987)). It hs logn+1 stges. The logic performs Kogge Stone on the odd numered its, nd then uses one more stge to ripple into the even positions. The Sklnsky or dividendconquer dder reduces the dely to log 2 N stges y computing intermedite prefixes long with the lrge group prefixes (J. Sklnsky (1960)). This comes t the expense of fnouts tht doule t ech level (8, 4, 2, 1). These high fnouts cuse poor performnce on wide dders unless the high fnout gtes re ppropritely sized or the criticl signls re uffered efore eing used for the intermedite prefixes. Trnsistor sizing cn cut into the regulrity of the lyout ecuse multiple sizes of ech cell re required, lthough the lrger gtes cn spred into djcent columns. 10
8 2.2 MULTIPLIER TOPOLOGIES Two clsses of prllel multipliers were defined in the 1960 s. The first clss of prllel multiplier use rectngulr rry of identicl cells which contins AND gte nd ddition logic to generte nd sum the prtil product its (J. C. Mjithi nd R. Kiti (1964)). These kinds of multipliers re clled rry multipliers nd they hve dely tht is proportionl to the multiplier input word size, i.e. O(N). Since rry multipliers hve regulr structure nd regulr wiring connectivity, it is esier to implement these t the lyout level (R P Pl Singh et l (2009)). The next clss of prllel multipliers termed column compression multipliers, uses counters or compressors to reduce the mtrix of prtil product rry to two words. Finlly crry propgte dder is used to sum these two words to get the finl product. The column compression multiplier hve dely proportionl to the logrithm of the multiplier word length, i.e. O(log N) So it is fster thn rry multiplier, ut due to its irregulr structure nd interconnections it is difficult to lyout ARRAY MULTIPLIERS A 4 y 4 rry multiplier structure is shown in Figure 2.6. Ech cell performs the two sic functions of prtil product genertion nd summtion. Hlf dders nd full dders re used to perform ddition function. An unsigned N y N rry multiplier requires N 2 + N cells, where N 2 contin n AND gte for prtil product genertion, 2N full dder nd N hlf dder to produce multiplier. The worst cse dely is (2N  2) c (Bickerstff K.C (2007)), where c is the worst cse dder dely. Here ll the products re generted in prllel nd collected through n rry of full dders nd hlf dders, finlly they re summed using CPA. Since its regulr structures, the rry multiplier tkes less mount of re, ut is slowest in terms of the ltency. In the 1950 s Booth lgorithm used in rry multipliers to perform two s complement multipliction (Andrew D. Booth (1951)). It computes the prtil products y exmining two multiplicnd its t time. Lter higher rdix modified Booth lgorithm ws introduced to improve the ltency performnce of the regulr Booth rry multiplier. 11
9 2,1 3,0 1,1 2,0 0,1 1,0 0,0 HA HA HA 3,1 2,2 1,2 0,2 FA FA FA 3,2 2,3 1,3 0,3 FA FA FA 3,3 FA FA HA p7 p6 p5 p4 p3 p2 p1 p0 Figure 2.6: Schemtic of 4 y 4 Arry Multiplier The Booth Rdix4 lgorithm (O. L. McSorley (1961)) reduces the numer of prtil products y hlf while keeping the circuit s complexity down to minimum. This result in fster less power in multipliction opertion. Booth Recoding mkes these dvntges possile y skipping clock cycles tht dd nothing new in the wy of product terms. The hrdwre implementtion for Rdix4 Booth Recoding technique use simple mux tht selects the correct shiftnddd opertion sed on the groupings of its found in the product register. The product register holds the multiplier. The multiplicnd nd the two s complement of the multiplicnd re dded sed on the recoding vlue. The directions for the rdix4 modified Booth recoding technique re shown in Tle
10 The three it decodes five possile opertions re dd 2*multiplicnd, dd multiplicnd, dd 0, sutrct multiplicnd, or sutrct 2*multiplicnd. It increses the hrdwre complexity, ut consumes only hlf the delys of the regulr Booth multiplier. It is possile to use higher rdices, such s rdix8 or rdix16, ut the dditionl complexity, due to nonpower of two multiples of the multiplicnd, compromises dely nd re improvements. Tle 2.1: Rdix4 Modified Booth Recoding i i1 i2 opertions Add Add multiplicnd Add multiplicnd Add 2* multiplicnd Sutrct 2* multiplicnd Sutrct multiplicnd Sutrct multiplicnd Sutrct 0 Another method ws proposed y Bugh nd Wooley (Chrles R. Bugh nd Bruce. A. Wooley (1973)) to hndle signed its. This technique hs een developed in order to design regulr multipliers suited for 2 s complement numers. Due to the dditionl two rows, it increses the mximum column height y two. Becuse of the dditionl two stges of prtil product reduction, it increses overll dely. A modified form of the Bugh nd Wooley method (ShinnRong Kung et l (2009)) is more commonly used ecuse it does not increse the mximum column height. The prtil product orgniztion of the modified BughWooley method is shown in Figure 2.7. The strtegy of orgniztion is follows, 1) Invert the MSB its of ech row except the ottom row. 2) Invert ll the its in ottom row, except the MSB it. 3) Add single one to the (N+1) th nd 2N th columns. The negtive prtil product its cn e generted using NAND gte insted of n AND gte, which my reduce the re slightly in CMOS. 13
11 # inverted it positions x7 x6 x5 x4 x3 x2 x1 x0 y7 y6 y5 y4 y3 y2 y1 y0 1 #p70 p60 p50 p40 p30 p20 p10 p00 #p71 p61 p51 p41 p31 p21 p11 p01 #p72 p62 p52 p42 p32 p22 p12 p02 #p73 p63 p53 p43 p33 p23 p13 p03 #p74 p64 p54 p44 p34 p24 p14 p04 #p75 p65 p55 p45 p35 p25 p15 p05 #p76 p66 p56 p46 p36 p26 p16 p06 1 p77 #p67 #p57 #p47 #p37 #p27 #p17 #p07 #s15 s14 s13 s12 s11 s10 s9 s8 s7 s6 s5 s4 s3 s2 s1 s0 Figure 2.7: Two s Complement Multipliction y Modified BughWooley Method COLUMN COMPRESSION MULTIPLIERS In 1964, Wllce (C.S.Wllce (1964)) introduced scheme for fst multipliction sed on using rry of full dders nd hlf dders. He used full dders for ll three its nd hlf dders for ll two its in the prtil products rry of multiplier to speed up the multipliction. Lter the Wllce s pproch ws modified y Ddd (Luigi Ddd (1965)) using counter plcement strtegy in the prtil product rry. Here the plcement of counters strts from the criticl pth in the prtil product rry. This plcement repets until we get finl two rows nd they re summed using crry propgte dder to get finl product. In oth Wllce nd Ddd methods, the dely of the multiplier is proportionl to the logrithm of the opernd wordlength. Reduced re pproch is n nother type of prtil product reduction method proposed for re optimiztion in column compression multipliers (K Andre et l (1993)). Another re reduction pproch is proposed y Wng s (Z. Wng et l (1995)). These methods re sed on strtegic utiliztion of full dders nd hlf dders to improve re reduction nd lyout, while mintining the fst speed of the Wllce nd Ddd designs. 14
12 Another prtil product reduction lgorithm sed on the unequl dely pths proposed y Oklodzij (V. G. Oklodzij (1995)). He defined the connectivity strtegy of slow inputs/outputs nd fst inputs/outputs in the criticl dely pths tht cn tolerte n increse in dely. A new orgniztion of the reduction tree, which is sed on the prtilproduct compression similr to the Ddd pproch, is proposed y Eriksson (H. Eriksson (2006)). The connectivity of the dding cells in the tringleshped HighPerformnce Multiplier (HPM) reduction tree is completely regulr PARTIAL PRODUCTS REDUCTION SCHEMES As shown in Figure 2.8, the multiplier strts with generting prtil products using AND gte rry nd reducing those to two rows using counters or compressors. It is good to understnd the difference etween counters nd compressors (V. G. Oklodzij nd D.Villeger (1995)). The counter counts the numer of ctive inputs nd the compressor (q:r) reduces q inputs to r outputs sed on the compression rtio. In this reserch we used counters for design multipliers, not used compressors. The column compression tree includes rry of counters or compressors. Finlly the two rows re dded using crry propgte dder to get finl product. Hyrid dder structure cn e used for crry propgte dder to perform fst ddition to get finl products. Multiplier N Multiplicnd N AND rry Column Compression Tree Finl Crry Propgte Adder 2N Figure 2.8: Bsic N y N unsigned prllel multiplier 15
13 Dot digrm is nottion for descriing multipliction column compression lgorithms. The symols used in dot digrms re listed elow, Ech dot  ech prtil product it Plin digonl line  ech full dder output Crossed digonl line  ech hlf dder output The dot digrm for 8 y 8 Wllce multiplier is shown in Figure 2.9. It ws constructed sed on the following Wllce lgorithm, 1) Tke ll three its in ech column nd dd them using full dder. 2) If there re two its left in ny of the column, dd them using hlf dder. 3) If there is just one it left in ny of the column, connect it to the next level. 4) Repet the steps 1 o 3 until get finl two rows. 5) Add the finl two numers using crry propgte dder to get the finl product. In ech stge of the reduction, Wllce performs preliminry grouping of prtil product rows into sets of three. Full dders nd hlf dders re then employed within ech three row set. In the 8 y 8 exmple, the counters shown in Stge 1 of the reduction re plced in four sections s determined y the preliminry grouping of prtil product its out of the AND rry into sets of three. If due to the preliminry grouping there is only one prtil product it, then tht it is directly moved down to the next stge. The reduction of the prtil product its in Stge 1 y the counters shown in Stge 2 demonstrtes tht rows which re not prt of three row set re moved down into the next stge without modifiction. 16
14 Figure 2.9: Dot Digrm of 8 y 8 Wllce Multiplier The complete prtil product reduction of 8 y 8 Wllce multiplier requires four stges (intermedite mtrix heights of 6, 4, 3, nd 2) nd uses 38 full dders nd 15 hlf dders. To complete the multipliction, n 11 it crrypropgte dder forms the finl product y dding the finl two rows of prtil product its shown in Stge 4. As mentioned erlier, lter the Ddd ws modified the Wllce s pproch using the counter plcement strtegy. Tle 2.2 indictes the numer of reduction stges sed on the numer of its in the Ddd multiplier. The reduction stges re determined from ottom (finl two rows) to top. In ech reduction stge the height of the mtrix is no more thn 1.5 times the height of its susequent mtrix. For exmple, 12 y 12 Ddd multiplier requires five reduction stges with intermedite heights of 9, 6, 4, 3 nd 2. 17
15 Tle 2.2: Reduction Strtegy for Ddd Multiplier Reduction Multiplier (N) Stges 3 Stge 1 4 Stge 2 5 <= N <= 6 Stge 3 7 <= N <= 9 Stge 4 10 <= N <= 13 Stge 5 14 <= N <= 19 Stge 6 20 <= N <= 28 Stge 7 29 <= N <= 42 Stge 8 43 <= N <= 63 Stge 9 64 <= N <= 94 Stge 10 The lgorithm used for Ddd multiplier is s follows: 1) Let d 1 = 2 nd d j+1 = 1.5 dj is the mtrix height for the j th stge from the finl two rows. It genertes the sequence: d 1 =2, d 2 =3, d 3 =4, etc. 2) For every column, use hlf dders nd full dders to ensure tht the numer of elements in ech column will e <= d j 3) Let j = j 1 nd repet step2 until you rech the mximum height of 2 it column. In Figure 2.10, the dot digrm for n8 y 8 Ddd multiplier is shown Figure The first six mtrix heights clculted using the recursive lgorithm re 2, 3, 4, 6 nd 9. Since this is 8 y 8 multiplier, the mtrix height of 9 is unnecessry. The next mtrix height to trget is 6. Stge 1 of prtil product reduction pplies full dders nd hlf dders only to the columns whose totl height is greter thn 6. In Stge 2, full dders nd hlf dders re only used in columns whose totl height is greter thn 4. Note tht when evluting column s height it is importnt to ccount for crries from the previous column. The 8 y 8 Ddd multiplier requires four reduction stges (mtrix heights of 6, 4, 3, nd 2) nd uses 35 full dders, 7 hlf dders, nd 14 it crrypropgte dder. 18
16 Figure 2.10: Dot Digrm of 8 y 8 Ddd Multiplier Reduced Are multiplier (K Andre et l (1993), K Andre et l (1995), K Andre et l (2001)) is n nother reduction scheme to optimize the re thn Wllce nd Ddd scheme. The dot digrm for 8 y 8 Reduced Are multiplier is shown in Figure 2.11.This multiplier requires four stges (mtrix heights of 6, 4, 3, nd 2) nd uses 35full dders, 7hlf dders, nd 10 it crrypropgte dder. The reduction method for the Reduced Are multiplier is: 1) For ech reduction stge, the numer of full dders used in ech column is i / 3, where i is the numer of its in column i. This provides the mximum column reduction in the numer of its entering the next stge. 2) Hlf dders re used only for the elow two conditions, 19
17 (i) When required to reduce the numer of its in column to the numer of its specified y the Ddd sequence (or) (ii) To reduce the rightmost column contining only two its. Reduced Are multiplier reduction scheme is especilly useful for pipelined multipliers, ecuse it reduces the required ltches in the prtil product reduction stges. This scheme cn e pplied for oth signed nd unsigned numers. Figure 2.11: Dot Digrm of 8 y 8 Reduced Are Multiplier 20
18 A fourth type of reduction scheme, which uses full dders nd hlf dders, is clled the High Performnce Multiplier (HPM) multiplier (H. Eriksson et l (2006)). The dot digrm for n 8 y 8 High Performnce Multiplier is shown in Figure This multiplier requires six stges (mtrix heights of 7, 6, 5, 4, 3, nd 2) nd uses 35full dders, 7hlf dders, nd 14 it crrypropgte dder. The reduction for ech stge in the High Performnce Multiplier is N1, where N is mtrix height of previous stge. Figure 2.12: Dot Digrm of 8 y 8 HPM Multiplier 21
19 A fifth type of prtil product reduction scheme hs een proposed y Wng, et l. (Z. Wng et l (1995)) to design more re efficient with shorted interconnections in the column compression multipliers. First he determines the lower ounds on the numer of dders required y column compression multiplier. Then the constrints hve een nlyzed for the distriution of dders to the different stges. Finlly he proposed technique tht ttempts to mximize re efficiency while reducing the numer of crossstge interconnections. The constrints for hlf dder nd full dder lloction in the column compression were nlyzed nd under these constrints, considerle flexiility for implementtion of the column compression multiplier nd choosing the length of the finl fst dder which yields higher re efficiency. In Wng s reserch, re efficiency of the column compression prt of the multiplier is defined s: N x 100% K.mx (N (k)) (2.9) where N is the totl numer of hlf dders nd full dders used in the reduction stges, K is the required numer of stges, nd N(k) is the numer of hlf dders nd full dders in stge k. The performnce of ny of these five multipliers Wllce, Ddd, Reduced Are, HPM nd Wng cn e improved y the proposed design techniques proposed in this reserch. 22
20 THE FINAL CARRYPROPAGATE ADDER All the fst dder structures were developed under the ssumption tht the input signls re rriving t the sme time. This ssumption is not relistic for mny plces like input rrivl profile from the multiplier prtil product summtion tree to the crry propgte dder. Therefore this reserch concerned out which one of the schemes for ddition is most dequte s crry propgte dder for the multiplier. The literture dels severl types of crrypropgte dders, including CSA, CLA, CSLA nd CSKA (R.Um et l (2012)). The dder structures hve een evluted nd rted sed on the dely, re nd numer of logic trnsitions (Thoms K. Cllwy nd Erl E. Swrtzlnder, Jr (1992)). More specificlly the work hs een done to evlute the power consumption of dders (Thoms K. Cllwy nd Erl E. Swrtzlnder, Jr (1993)). It is well known tht the signls from column compression tree pplied to the inputs of the crry propgte dder rrive first t the ends of the crry propgte dder nd the lst ones re those in the middle of the crry propgte dder. So the determintion of the exct rrivl time to crry propgte dder is of prime importnce in the design of the optiml finl dder. To etter select nd design dders for column compression multipliers Oklodzij nlyzed the input rrivl times to the finl dder (V. G. Oklodzij nd D.Villeger (1995), V. G. Oklodzij (1995)) nd he suggests using either vrile lock dder or RCA to sum the erly LSB vlues, CLA to sum the middle region of its, nd either conditionl sum dder or CSLA to sum the erly MSB vlues. Since RCA hs simple nd regulr structure, it consumes lesser power nd is re efficient thn ll other existing dders. But ech stge in RCA genertes sum only fter receiving the crry it from the preceding stge it pirs. So it leds to lrge crry propgtion dely. The rrivl profile s shown y Oklodzij (V. G. Oklodzij nd D.Villeger (1995)) nd Blsurhmnym (Blsurhmnym et l (2012)), hs positive slope from the LSB region to middle region of the prtil products. Even though the crry it rrives fster from the preceding stge of the finl ddition, the rrivl of true vlues from the prtil products re slower in the positive slope region. So the fst dder is not est choice in this region nd the RCA is est choice in the positive slope. 23
21 But this slope is not lwys positive in the entire multiplier region. It hs constnt slope in the middle region nd negtive slope in the MSB side of the prtil products. So determintion of the suitle dder in ech region would led to optiml performnce of the multipliers. Bsed on the different rrivl profile region of the prtil products, this reserch proposed hyrid crry propgte dder structure for prllel multipliers which consumes lesser power, re efficient thn the regulr CSLA, nd fster thn the CSA. This enles optiml performnce in the finl ddition for the multipliers proposed in this reserch. 24
CHAPTER 2 LITERATURE STUDY
CHAPTER LITERATURE STUDY. Introduction Multipliction involves two bsic opertions: the genertion of the prtil products nd their ccumultion. Therefore, there re two possible wys to speed up the multipliction:
More informationDesign and Development of 8Bits Fast Multiplier for Low Power Applications
IACSIT Interntionl Journl of Engineering nd Technology, Vol. 4, No. 6, Decemer 22 Design nd Development of 8Bits Fst Multiplier for Low Power Applictions Vsudev G. nd Rjendr Hegdi, Memer, IACSIT proportionl
More informationAreaTime Efficient DigitSerialSerial Two s Complement Multiplier
AreTime Efficient DigitSerilSeril Two s Complement Multiplier Essm Elsyed nd Htem M. ElBoghddi Computer Engineering Deprtment, Ciro University, Egypt Astrct  Multipliction is n importnt primitive
More informationSequential Logic (2) Synchronous vs Asynchronous Sequential Circuit. Clock Signal. Synchronous Sequential Circuits. FSM Overview 9/10/12
9//2 Sequentil (2) ENGG5 st Semester, 22 Dr. Hden So Deprtment of Electricl nd Electronic Engineering http://www.eee.hku.hk/~engg5 Snchronous vs Asnchronous Sequentil Circuit This Course snchronous Sequentil
More informationMixed CMOS PTL Adders
Anis do XXVI Congresso d SBC WCOMPA l I Workshop de Computção e Aplicções 14 20 de julho de 2006 Cmpo Grnde, MS Mixed CMOS PTL Adders Déor Mott, Reginldo d N. Tvres Engenhri em Sistems Digitis Universidde
More informationDIGITAL multipliers [1], [2] are the core components of
World Acdemy of Science, Engineering nd Technology 9 8 A ReducedBit Multipliction Algorithm for Digitl Arithmetic Hrpreet Singh Dhillon nd Ahijit Mitr Astrct A reducedit multipliction lgorithm sed on
More informationGeometric quantities for polar curves
Roerto s Notes on Integrl Clculus Chpter 5: Bsic pplictions of integrtion Section 10 Geometric quntities for polr curves Wht you need to know lredy: How to use integrls to compute res nd lengths of regions
More informationTo provide data transmission in indoor
Hittite Journl of Science nd Engineering, 2018, 5 (1) 2529 ISSN NUMBER: 21484171 DOI: 10.17350/HJSE19030000074 A New Demodultor For Inverse Pulse Position Modultion Technique Mehmet Sönmez Osmniye Korkut
More informationKirchhoff s Rules. Kirchhoff s Laws. Kirchhoff s Rules. Kirchhoff s Laws. Practice. Understanding SPH4UW. Kirchhoff s Voltage Rule (KVR):
SPH4UW Kirchhoff s ules Kirchhoff s oltge ule (K): Sum of voltge drops round loop is zero. Kirchhoff s Lws Kirchhoff s Current ule (KC): Current going in equls current coming out. Kirchhoff s ules etween
More informationCS 135: Computer Architecture I. Boolean Algebra. Basic Logic Gates
Bsic Logic Gtes : Computer Architecture I Boolen Algebr Instructor: Prof. Bhgi Nrhri Dept. of Computer Science Course URL: www.ses.gwu.edu/~bhgiweb/cs35/ Digitl Logic Circuits We sw how we cn build the
More informationDesign and implementation of a highspeed bitserial SFQ adder based on the binary decision diagram
INSTITUTE OFPHYSICS PUBLISHING Supercond. Sci. Technol. 16 (23) 1497 152 SUPERCONDUCTORSCIENCE AND TECHNOLOGY PII: S953248(3)671113 Design nd implementtion of highspeed itseril SFQ dder sed on the
More informationStudent Book SERIES. Patterns and Algebra. Name
E Student Book 3 + 7 5 + 5 Nme Contents Series E Topic Ptterns nd functions (pp. ) identifying nd creting ptterns skip counting completing nd descriing ptterns predicting repeting ptterns predicting growing
More informationSolutions to exercise 1 in ETS052 Computer Communication
Solutions to exercise in TS52 Computer Communiction 23 Septemer, 23 If it occupies millisecond = 3 seconds, then second is occupied y 3 = 3 its = kps. kps If it occupies 2 microseconds = 2 6 seconds, then
More informationMath Circles Finite Automata Question Sheet 3 (Solutions)
Mth Circles Finite Automt Question Sheet 3 (Solutions) Nickols Rollick nrollick@uwterloo.c Novemer 2, 28 Note: These solutions my give you the nswers to ll the prolems, ut they usully won t tell you how
More informationModule 9. DC Machines. Version 2 EE IIT, Kharagpur
Module 9 DC Mchines Version EE IIT, Khrgpur esson 40 osses, Efficiency nd Testing of D.C. Mchines Version EE IIT, Khrgpur Contents 40 osses, efficiency nd testing of D.C. mchines (esson40) 4 40.1 Gols
More informationMOS Transistors. Silicon Lattice
rin n Width W chnnel ptype (doped) sustrte MO Trnsistors n Gte Length L O 2 (insultor) ource Conductor (poly) rin rin Gte nmo trnsistor Gte ource pmo trnsistor licon sustrte doped with impurities dding
More informationISSCC 2006 / SESSION 21 / ADVANCED CLOCKING, LOGIC AND SIGNALING TECHNIQUES / 21.5
21.5 A 1.1GHz ChrgeRecovery Logic Visvesh Sthe, JungYing Chueh, Mrios Ppefthymiou University of Michign, Ann Aror, MI Boost Logic is chrgerecovery circuit fmily cple of operting t GHzclss frequencies
More informationFirst Round Solutions Grades 4, 5, and 6
First Round Solutions Grdes 4, 5, nd 1) There re four bsic rectngles not mde up of smller ones There re three more rectngles mde up of two smller ones ech, two rectngles mde up of three smller ones ech,
More informationA COMPARISON OF CIRCUIT IMPLEMENTATIONS FROM A SECURITY PERSPECTIVE
A COMPARISON OF CIRCUIT IMPLEMENTATIONS FROM A SECURITY PERSPECTIVE Mster Thesis Division of Electronic Devices Deprtment of Electricl Engineering Linköping University y Timmy Sundström LITHISYEX05/3698SE
More informationDataflow Language Model. DataFlow Models. Applications of Dataflow. Dataflow Languages. Kahn process networks. A Kahn Process (1)
The slides contin revisited mterils from: Peter Mrwedel, TU Dortmund Lothr Thiele, ETH Zurich Frnk Vhid, University of liforni, Riverside Dtflow Lnguge Model Drsticlly different wy of looking t computtion:
More informationAsynchronous DataDriven Circuit Synthesis
Asynchronous DtDriven Circuit Synthesis Sm Tylor, Doug Edwrds, Luis A Pln, Senior Memer, IEEE nd Luis A. Trzon D., Student Memer, IEEE Astrct A method is descried for synthesising synchronous circuits
More informationThe Design and Verification of A HighPerformance LowControlOverhead Asynchronous Differential Equation Solver
he Design nd Verifiction of A HighPerformnce LowControlOverhed Asynchronous Differentil Eqution Solver Kenneth Y. Yun, Memer, IEEE, Peter A. Beerel, Memer, IEEE, Vid Vkilotojr, Student Memer, IEEE,
More informationMultibeam antennas in a broadband wireless access system
Multiem ntenns in rodnd wireless ccess system Ulrik Engström, Mrtin Johnsson, nders Derneryd nd jörn Johnnisson ntenn Reserch Center Ericsson Reserch Ericsson SE4 84 Mölndl Sweden Emil: ulrik.engstrom@ericsson.com,
More informationAutomatic Synthesis of Compressor Trees: Reevaluating Large Counters
Automtic Snthesis of Compressor Trees: Reevluting Lrge Counters Aj K. Verm AjKumr.Verm@epfl.ch Polo Ienne Polo.Ienne@epfl.ch Ecole Poltechnique Fédérle de Lusnne (EPFL) School of Computer nd Communiction
More informationUnderstanding Basic Analog Ideal Op Amps
Appliction Report SLAA068A  April 2000 Understnding Bsic Anlog Idel Op Amps Ron Mncini Mixed Signl Products ABSTRACT This ppliction report develops the equtions for the idel opertionl mplifier (op mp).
More informationECE 274 Digital Logic. Digital Design. Datapath Components Shifters, Comparators, Counters, Multipliers Digital Design
ECE 27 Digitl Logic Shifters, Comprtors, Counters, Multipliers Digitl Design..7 Digitl Design Chpter : Slides to ccompny the textbook Digitl Design, First Edition, by Frnk Vhid, John Wiley nd Sons Publishers,
More information10.4 AREAS AND LENGTHS IN POLAR COORDINATES
65 CHAPTER PARAMETRIC EQUATINS AND PLAR CRDINATES.4 AREAS AND LENGTHS IN PLAR CRDINATES In this section we develop the formul for the re of region whose oundry is given y polr eqution. We need to use the
More informationThreePhase Synchronous Machines The synchronous machine can be used to operate as: 1. Synchronous motors 2. Synchronous generators (Alternator)
ThreePhse Synchronous Mchines The synchronous mchine cn be used to operte s: 1. Synchronous motors 2. Synchronous genertors (Alterntor) Synchronous genertor is lso referred to s lterntor since it genertes
More informationThe Discussion of this exercise covers the following points:
Exercise 4 Bttery Chrging Methods EXERCISE OBJECTIVE When you hve completed this exercise, you will be fmilir with the different chrging methods nd chrgecontrol techniques commonly used when chrging NiMI
More informationExperiment 3: NonIdeal Operational Amplifiers
Experiment 3: NonIdel Opertionl Amplifiers Fll 2009 Equivlent Circuits The bsic ssumptions for n idel opertionl mplifier re n infinite differentil gin ( d ), n infinite input resistnce (R i ), zero output
More informationSOLVING TRIANGLES USING THE SINE AND COSINE RULES
Mthemtics Revision Guides  Solving Generl Tringles  Sine nd Cosine Rules Pge 1 of 17 M.K. HOME TUITION Mthemtics Revision Guides Level: GCSE Higher Tier SOLVING TRIANGLES USING THE SINE AND COSINE RULES
More informationCHAPTER 3 AMPLIFIER DESIGN TECHNIQUES
CHAPTER 3 AMPLIFIER DEIGN TECHNIQUE 3.0 Introduction olidstte microwve mplifiers ply n importnt role in communiction where it hs different pplictions, including low noise, high gin, nd high power mplifiers.
More informationApplication Note. Differential Amplifier
Appliction Note AN367 Differentil Amplifier Author: Dve n Ess Associted Project: Yes Associted Prt Fmily: CY8C9x66, CY8C7x43, CY8C4x3A PSoC Designer ersion: 4. SP3 Abstrct For mny sensing pplictions, desirble
More information1 tray of toffee 1 bar of toffee. 10 In the decimal number, 0 7, the 7 refers to 7 tenths or
Chpter 3 Deciml Numers Do you know wht DECIMAL is? In chpter, we delt with units, s, 0 s nd 00 s. When you tke single unit nd divide it into (or 0 or 00) its, wht we then hve re deciml frctions of whole
More informationExperiment 3: NonIdeal Operational Amplifiers
Experiment 3: NonIdel Opertionl Amplifiers 9/11/06 Equivlent Circuits The bsic ssumptions for n idel opertionl mplifier re n infinite differentil gin ( d ), n infinite input resistnce (R i ), zero output
More informationAlgorithms for Memory Hierarchies Lecture 14
Algorithms for emory Hierrchies Lecture 4 Lecturer: Nodri Sitchinv Scribe: ichel Hmnn Prllelism nd Cche Obliviousness The combintion of prllelism nd cche obliviousness is n ongoing topic of reserch, in
More informationExperiment 8 Series DC Motor (II)
Ojectives To control the speed of loded series dc motor y chnging rmture voltge. To control the speed of loded series dc motor y dding resistnce in prllel with the rmture circuit. To control the speed
More informationMETHOD OF LOCATION USING SIGNALS OF UNKNOWN ORIGIN. Inventor: Brian L. Baskin
METHOD OF LOCATION USING SIGNALS OF UNKNOWN ORIGIN Inventor: Brin L. Bskin 1 ABSTRACT The present invention encompsses method of loction comprising: using plurlity of signl trnsceivers to receive one or
More informationINSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad
Hll Ticket No Question Pper Code: AEC009 INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigl, Hyderd  500 043 MODEL QUESTION PAPER Four Yer B.Tech V Semester End Exmintions, Novemer  2018 Regultions:
More informationCS2204 DIGITAL LOGIC & STATE MACHINE DESIGN SPRING 2005
CS2204 DIGITAL LOGIC & STATE MACHINE DESIGN SPRING 2005 EXPERIMENT 1 FUNDAMENTALS 1. GOALS : Lern how to develop cr lrm digitl circuit during which the following re introduced : CS2204 l fundmentls, nd
More information& Y Connected resistors, Light emitting diode.
& Y Connected resistors, Light emitting diode. Experiment # 02 Ojectives: To get some hndson experience with the physicl instruments. To investigte the equivlent resistors, nd Y connected resistors, nd
More informationOn the Description of Communications Between Software Components with UML
On the Description of Communictions Between Softwre Components with UML Zhiwei An Dennis Peters Fculty of Engineering nd Applied Science Memoril University of Newfoundlnd St. John s NL A1B 3X5 zhiwei@engr.mun.c
More informationUse of compiler optimization of software bypassing as a method to improve energy efficiency of exposed data path architectures
Guzm et l. EURASIP Journl on Emedded Systems 213, 213:9 RESEARCH Open Access Use of compiler optimiztion of softwre ypssing s method to improve energy efficiency of exposed dt pth rchitectures Vldimír
More informationMAXIMUM FLOWS IN FUZZY NETWORKS WITH FUNNELSHAPED NODES
MAXIMUM FLOWS IN FUZZY NETWORKS WITH FUNNELSHAPED NODES Romn V. Tyshchuk Informtion Systems Deprtment, AMI corportion, Donetsk, Ukrine Emil: rt_science@hotmil.com 1 INTRODUCTION During the considertion
More informationDirect Current Circuits. Chapter Outline Electromotive Force 28.2 Resistors in Series and in Parallel 28.3 Kirchhoff s Rules 28.
P U Z Z L E R If ll these pplinces were operting t one time, circuit reker would proly e tripped, preventing potentilly dngerous sitution. Wht cuses circuit reker to trip when too mny electricl devices
More informationSoft switched DCDC PWM Converters
Soft switched DCDC PWM Converters Mr.M. Prthp Rju (), Dr. A. Jy Lkshmi () Abstrct This pper presents n upgrded soft switching technique zero current trnsition (ZCT), which gives better turn off chrcteristics
More informationarxiv: v1 [cs.cc] 29 Mar 2012
Solving Mhjong Solitire ords with peeking Michiel de Bondt rxiv:1203.6559v1 [cs.cc] 29 Mr 2012 Decemer 22, 2013 Astrct We first prove tht solving Mhjong Solitire ords with peeking is NPcomplete, even if
More informationPennsylvania State University. University Park, PA only simple two or three input gates (e.g., AND/NAND,
Highthroughput nd Lowpower DSP Using lockedmos ircuitry Mnjit Borh Robert Michel Owens Deprtment of omputer Science nd Engineering Pennsylvni Stte University University Prk, PA 16802 Mry Jne Irwin Abstrct
More informationA New Algorithm to Compute Alternate Paths in Reliable OSPF (ROSPF)
A New Algorithm to Compute Alternte Pths in Relile OSPF (ROSPF) Jin Pu *, Eric Mnning, Gholmli C. Shoj, Annd Srinivsn ** PANDA Group, Computer Science Deprtment University of Victori Victori, BC, Cnd Astrct
More informationImplementation of Different Architectures of Forward 4x4 Integer DCT For H.264/AVC Encoder
Implementtion of Different Architectures of Forwrd 4x4 Integer DCT For H.64/AVC Encoder Bunji Antoinette Ringnyu, Ali Tngel, Emre Krulut 3 Koceli University, Institute of Science nd Technology, Koceli,
More information(CATALYST GROUP) B"sic Electric"l Engineering
(CATALYST GROUP) B"sic Electric"l Engineering 1. Kirchhoff s current l"w st"tes th"t (") net current flow "t the junction is positive (b) Hebr"ic sum of the currents meeting "t the junction is zero (c)
More informationLecture 20. Intro to line integrals. Dan Nichols MATH 233, Spring 2018 University of Massachusetts.
Lecture 2 Intro to line integrls Dn Nichols nichols@mth.umss.edu MATH 233, Spring 218 University of Msschusetts April 12, 218 (2) onservtive vector fields We wnt to determine if F P (x, y), Q(x, y) is
More informationUniversity of North CarolinaCharlotte Department of Electrical and Computer Engineering ECGR 4143/5195 Electrical Machinery Fall 2009
Problem 1: Using DC Mchine University o North CrolinChrlotte Deprtment o Electricl nd Computer Engineering ECGR 4143/5195 Electricl Mchinery Fll 2009 Problem Set 4 Due: Thursdy October 8 Suggested Reding:
More informationJDT EFFECTIVE METHOD FOR IMPLEMENTATION OF WALLACE TREE MULTIPLIER USING FAST ADDERS
JDT0022013 EFFECTIVE METHOD FOR IMPLEMENTATION OF WALLACE TREE MULTIPLIER USING FAST ADDERS E. Prakash 1, R. Raju 2, Dr.R. Varatharajan 3 1 PG Student, Department of Electronics and Communication Engineeering
More informationEE Controls Lab #2: Implementing StateTransition Logic on a PLC
Objective: EE 44  Controls Lb #2: Implementing Stternsition Logic on PLC ssuming tht speed is not of essence, PLC's cn be used to implement stte trnsition logic. he dvntge of using PLC over using hrdwre
More informationExample. Check that the Jacobian of the transformation to spherical coordinates is
lss, given on Feb 3, 2, for Mth 3, Winter 2 Recll tht the fctor which ppers in chnge of vrible formul when integrting is the Jcobin, which is the determinnt of mtrix of first order prtil derivtives. Exmple.
More informationA Practical DPA Countermeasure with BDD Architecture
A Prcticl DPA Countermesure with BDD Architecture Toru Akishit, Msnou Ktgi, Yoshikzu Miyto, Asmi Mizuno, nd Kyoji Shiutni System Technologies Lortories, Sony Corportion, 7 Konn, Mintoku, Tokyo 875,
More informationA Novel Back EMF Zero Crossing Detection of Brushless DC Motor Based on PWM
A ovel Bck EMF Zero Crossing Detection of Brushless DC Motor Bsed on PWM Zhu Bopeng Wei Hifeng School of Electricl nd Informtion, Jingsu niversity of Science nd Technology, Zhenjing 1003 Chin) Abstrct:
More informationHigh Speed OnChip Interconnects: Trade offs in Passive Termination
High Speed OnChip Interconnects: Trde offs in Pssive Termintion Rj Prihr University of Rochester, NY, USA prihr@ece.rochester.edu Abstrct In this pper, severl pssive termintion schemes for high speed
More informationThreshold Logic Computing: MemristiveCMOS Circuits for Fast Fourier Transform and Vedic Multiplication
1 Threshold Logic Computing: MemristiveCMOS Circuits for Fst Fourier Trnsform nd edic Multipliction Alex Pppchen Jmes, Dinesh S. Kumr, nd Arun Ajyn Abstrct Brin inspired circuits cn provide n lterntive
More informationConvolutional Networks. Lecture slides for Chapter 9 of Deep Learning Ian Goodfellow
Convolutionl Networks Lecture slides for Chpter 9 of Deep Lerning In Goodfellow 20160912 Convolutionl Networks Scle up neurl networks to process very lrge imges / video sequences Sprse connections Prmeter
More informationABB STOTZKONTAKT. ABB ibus EIB Current Module SM/S Intelligent Installation Systems. User Manual SM/S In = 16 A AC Un = 230 V AC
User Mnul ntelligent nstlltion Systems A B 1 2 3 4 5 6 7 8 30 ma 30 ma n = AC Un = 230 V AC 30 ma 9 10 11 12 C ABB STOTZKONTAKT Appliction Softwre Current Vlue Threshold/1 Contents Pge 1 Device Chrcteristics...
More informationAnalysis of circuits containing active elements by using modified T  graphs
Anlsis of circuits contining ctive elements using modified T  grphs DALBO BOLEK *) nd EA BOLKOA**) Deprtment of Telecommunictions *) dioelectronics **) Brno Universit of Technolog Purknov 8, 6 Brno CECH
More informationMONOCHRONICLE STRAIGHT
UPDATED 092010 HYDROCARBON Hydrocrbon is ponchostyle cowl in bulkyweight yrn, worked in the round. It ws designed to be s prcticl s it is stylish, with shping tht covers the neck nd shoulders nd the
More informationSpiral Tilings with Ccurves
Spirl Tilings with curves Using ombintorics to Augment Trdition hris K. Plmer 19 North Albny Avenue hicgo, Illinois, 0 chris@shdowfolds.com www.shdowfolds.com Abstrct Spirl tilings used by rtisns through
More informationOpen Access A Novel Parallel Currentsharing Control Method of Switch Power Supply
Send Orders for Reprints to reprints@enthmscience.e 170 The Open Electricl & Electronic Engineering Journl, 2014, 8, 170177 Open Access A Novel Prllel Currentshring Control Method of Switch Power Supply
More informationApril 9, 2000 DIS chapter 10 CHAPTER 3 : INTEGRATED PROCESSORLEVEL ARCHITECTURES FOR REALTIME DIGITAL SIGNAL PROCESSING
April 9, 2000 DIS chpter 0 CHAPTE 3 : INTEGATED POCESSOLEVEL ACHITECTUES FO EALTIME DIGITAL SIGNAL POCESSING April 9, 2000 DIS chpter 3.. INTODUCTION The purpose of this chpter is twofold. Firstly, bsic
More informationDigital Design. Sequential Logic Design  Controllers. Copyright 2007 Frank Vahid
Digitl Design Sequentil Logic Design  Controllers Slides to ccompny the tetook Digitl Design, First Edition, y, John Wiley nd Sons Pulishers, 27. http://www.ddvhid.com Copyright 27 Instructors of courses
More informationA Highly Efficient Carry Select Adder
IJSTE  International Journal of Science Technology & Engineering Volume 2 Issue 4 October 2015 ISSN (online): 2349784X A Highly Efficient Carry Select Adder Shiya Andrews V PG Student Department of Electronics
More informationThe Math Learning Center PO Box 12929, Salem, Oregon Math Learning Center
Resource Overview Quntile Mesure: Skill or Concept: 300Q Model the concept of ddition for sums to 10. (QT N 36) Model the concept of sutrction using numers less thn or equl to 10. (QT N 37) Write ddition
More informationAlternatingCurrent Circuits
chpter 33 AlterntingCurrent Circuits 33.1 AC Sources 33.2 esistors in n AC Circuit 33.3 Inductors in n AC Circuit 33.4 Cpcitors in n AC Circuit 33.5 The LC Series Circuit 33.6 Power in n AC Circuit 33.7
More informationStudent Book SERIES. Fractions. Name
D Student Book Nme Series D Contents Topic Introducing frctions (pp. ) modelling frctions frctions of collection compring nd ordering frctions frction ingo pply Dte completed / / / / / / / / Topic Types
More informationAn Optimized Wallace Tree Multiplier using Parallel Prefix HanCarlson Adder for DSP Processors
An Optimized Wallace Tree Multiplier using Parallel Prefix HanCarlson Adder for DSP Processors T.N.Priyatharshne Prof. L. Raja, M.E, (Ph.D) A. Vinodhini ME VLSI DESIGN Professor, ECE DEPT ME VLSI DESIGN
More informationDiscontinued AN6262N, AN6263N. (planed maintenance type, maintenance type, planed discontinued typed, discontinued type)
ICs for Cssette, Cssette Deck ANN, ANN Puse Detection s of Rdio Cssette, Cssette Deck Overview The ANN nd the ANN re the puse detection integrted circuits which select the progrm on the cssette tpe. In
More informationA Development of EarthingResistanceEstimation Instrument
A Development of ErthingResistnceEstimtion Instrument HITOSHI KIJIMA Abstrct:  Whenever erth construction work is done, the implnted number nd depth of electrodes hve to be estimted in order to obtin
More informationSection 16.3 Double Integrals over General Regions
Section 6.3 Double Integrls over Generl egions Not ever region is rectngle In the lst two sections we considered the problem of integrting function of two vribles over rectngle. This sitution however is
More informationEngineertoEngineer Note
EngineertoEngineer Note EE236 Technicl notes on using Anlog Devices DSPs, processors nd development tools Contct our technicl support t dsp.support@nlog.com nd t dsptools.support@nlog.com Or visit our
More informationNetwork Theorems. Objectives 9.1 INTRODUCTION 9.2 SUPERPOSITION THEOREM
M09_BOYL3605_13_S_C09.indd Pge 359 24/11/14 1:59 PM f403 /204/PH01893/9780133923605_BOYLSTAD/BOYLSTAD_NTRO_CRCUT_ANALYSS13_S_978013... Network Theorems Ojectives Become fmilir with the superposition theorem
More informationExperiment 3: The research of Thevenin theorem
Experiment 3: The reserch of Thevenin theorem 1. Purpose ) Vlidte Thevenin theorem; ) Mster the methods to mesure the equivlent prmeters of liner twoterminl ctive. c) Study the conditions of the mximum
More informationInterference Cancellation Method without Feedback Amount for Three Users Interference Channel
Open Access Librry Journl 07, Volume, e57 ISSN Online: 97 ISSN Print: 9705 Interference Cncelltion Method without Feedbc Amount for Three Users Interference Chnnel Xini Tin, otin Zhng, Wenie Ji School
More informationExercise 11. The Sine Wave EXERCISE OBJECTIVE DISCUSSION OUTLINE. Relationship between a rotating phasor and a sine wave DISCUSSION
Exercise 11 The Sine Wve EXERCISE OBJECTIVE When you hve completed this exercise, you will be fmilir with the notion of sine wve nd how it cn be expressed s phsor rotting round the center of circle. You
More informationPatterns and Algebra
Student Book Series D Mthletis Instnt Workooks Copyright Series D Contents Topi Ptterns nd funtions identifying nd reting ptterns skip ounting ompleting nd desriing ptterns numer ptterns in tles growing
More informationSynchronous Machine Parameter Measurement
Synchronous Mchine Prmeter Mesurement 1 Synchronous Mchine Prmeter Mesurement Introduction Wound field synchronous mchines re mostly used for power genertion but lso re well suited for motor pplictions
More informationSynchronous Machine Parameter Measurement
Synchronous Mchine Prmeter Mesurement 1 Synchronous Mchine Prmeter Mesurement Introduction Wound field synchronous mchines re mostly used for power genertion but lso re well suited for motor pplictions
More informationTranslate and Classify Conic Sections
TEKS 9.6 A.5.A, A.5.B, A.5.D, A.5.E Trnslte nd Clssif Conic Sections Before You grphed nd wrote equtions of conic sections. Now You will trnslte conic sections. Wh? So ou cn model motion, s in E. 49. Ke
More informationCompared to generators DC MOTORS. Back e.m.f. Back e.m.f. Example. Example. The construction of a d.c. motor is the same as a d.c. generator.
Compred to genertors DC MOTORS Prepred by Engr. JP Timol Reference: Electricl nd Electronic Principles nd Technology The construction of d.c. motor is the sme s d.c. genertor. the generted e.m.f. is less
More informationTh ELI1 09 Broadband Processing of West of Shetland Data
Th ELI 9 Brodnd Processing of West of Shetlnd Dt R. Telling* (Dolphin Geophysicl Limited), N. Riddlls (Dolphin Geophysicl Ltd), A. Azmi (Dolphin Geophysicl Ltd), S. Grion (Dolphin Geophysicl Ltd) & G.
More informationPolar Coordinates. July 30, 2014
Polr Coordintes July 3, 4 Sometimes it is more helpful to look t point in the xyplne not in terms of how fr it is horizontlly nd verticlly (this would men looking t the Crtesin, or rectngulr, coordintes
More informationEQ: What are the similarities and differences between matrices and real numbers?
Unit 4 Lesson 1 Essentil Question Stndrds Objectives Vocbulry Mtrices Mtrix Opertions Wht re the similrities nd differences between mtrices nd rel numbers? M.ALGII.2.4 Unit 4: Lesson 1 Describe how you
More informationControl of highfrequency AC link electronic transformer
Control of highfrequency AC link electronic trnsformer H. Krishnswmi nd V. Rmnrynn Astrct: An isolted highfrequency link AC/AC converter is termed n electronic trnsformer. The electronic trnsformer hs
More informationPerformance Comparison between Network Coding in Space and Routing in Space
Performnce omprison etween Network oding in Spce nd Routing in Spce Yunqing Ye, Xin Hung, Ting Wen, Jiqing Hung nd lfred Uwitonze eprtment of lectronics nd Informtion ngineering, Huzhong University of
More informationTriangles and parallelograms of equal area in an ellipse
1 Tringles nd prllelogrms of equl re in n ellipse Roert Buonpstore nd Thoms J Osler Mthemtics Deprtment RownUniversity Glssoro, NJ 0808 USA uonp0@studentsrownedu osler@rownedu Introduction In the pper
More informationPowerAware FPGA Logic Synthesis Using Binary Decision Diagrams
PowerAwre FPGA Logic Synthesis Using Binry Decision Digrms Kevin Oo Tinmung, Dvid Howlnd, nd Russell Tessier Deprtment of Electricl nd Computer Engineering University of Msschusetts Amherst, MA 01003
More informationAn Optimized Implementation of CSLA and CLLA for 32bit Unsigned Multiplier Using Verilog
An Optimized Implementation of CSLA and CLLA for 32bit Unsigned Multiplier Using Verilog 1 P.Sanjeeva Krishna Reddy, PG Scholar in VLSI Design, 2 A.M.Guna Sekhar Assoc.Professor 1 appireddigarichaitanya@gmail.com,
More informationEET 438a Automatic Control Systems Technology Laboratory 5 Control of a Separately Excited DC Machine
EE 438 Automtic Control Systems echnology bortory 5 Control of Seprtely Excited DC Mchine Objective: Apply proportionl controller to n electromechnicl system nd observe the effects tht feedbck control
More informationDomination and Independence on Square Chessboard
Engineering nd Technology Journl Vol. 5, Prt, No. 1, 017 A.A. Omrn Deprtment of Mthemtics, College of Eduction for Pure Science, University of bylon, bylon, Irq pure.hmed.omrn@uobby lon.edu.iq Domintion
More informationLab 8. Speed Control of a D.C. motor. The Motor Drive
Lb 8. Speed Control of D.C. motor The Motor Drive Motor Speed Control Project 1. Generte PWM wveform 2. Amplify the wveform to drive the motor 3. Mesure motor speed 4. Mesure motor prmeters 5. Control
More informationFaster and Low Power Twin Precision Multiplier
Faster and Low Twin Precision V. Sreedeep, B. Ramkumar and Harish M Kittur Abstract In this work faster unsigned multiplication has been achieved by using a combination High Performance Multiplication
More informationLecture 16: Four Quadrant operation of DC Drive (or) TYPE E Four Quadrant chopper Fed Drive: Operation
Lecture 16: Four Qudrnt opertion of DC Drive (or) TYPE E Four Qudrnt chopper Fed Drive: Opertion The rmture current I is either positive or negtive (flow in to or wy from rmture) the rmture voltge is lso
More informationFrancis Gaspalou Second edition of February 10, 2012 (First edition on January 28, 2012) HOW MANY SQUARES ARE THERE, Mr TARRY?
Frncis Gslou Second edition of Ferury 10, 2012 (First edition on Jnury 28, 2012) HOW MANY SQUARES ARE THERE, Mr TARRY? ABSTRACT In this er, I enumerte ll the 8x8 imgic sures given y the Trry s ttern. This
More information