Some Modular Adders and Multipliers for Field Programmable Gate Arrays
|
|
- Andrew Blankenship
- 5 years ago
- Views:
Transcription
1 Some Modular Adders ad Multipliers for Field Programmable Gate Arras Jea-Luc Beuchat Laboratoire de l Iformatique du Parallélisme (CNRS, ENSL, INRIA) 46, Allée d Italie F Lo Cede 7 Jea-Luc.Beuchat@es-lo.fr Abstract This paper is devoted to the stud of umber represetatios ad algorithms leadig to efficiet implemetatios of modular adders ad multipliers o recet Field Programmable Arras. Our hardware operators take advatage of the buildig blocks available i such devices: carrpropagate adders, memor blocks, ad sometimes embedded multipliers. The first part of the paper describes three basic methodologies to carr out a modulo m additio ad presets i more details the desig of modulo (2 ± ) adders. The major result is a ovel modulo (2 +) additio algorithm leadig to a area-time efficiet implemetatio of this arithmetic operatio o FPGAs. The secod part describes a modulo m multiplicatio algorithm ivolvig small multipliers ad memor blocks, ad modulo (2 +) multipliers based o Ma s algorithm. We also suggest some improvemets of this operator i order to perform a multiplicatio i the group (Z 2 +, ). Itroductio Modular arithmetic plas a crucial role i various fields such as residue umber sstem arithmetic or crptograph. Several algorithms for modular additio ad multiplicatio have bee proposed ad umerous papers describe both theoretical ad practical results (see for istace [4, 6, 7]). Those algorithms are geerall desiged for stadard itegrated circuits ad are based o ver low-level basic elemets such as NAND or XOR gates. However, recet Field Programmable Gate Arras (FPGA) embed dedicated carr logic, memor blocks, ad sometimes small multipliers. Arithmetic operators takig advatage of these ew buildig blocks could outperform classic architectures. A recet stud of usiged multiplicatio ad divisio o Virte-II devices has alread show that embedded multipliers allow sigificat speed improvemets compared to stadard solutios ol based o Cofigurable Logic Blocks (CLB) [2]. This paper is devoted to the stud of umber represetatios ad algorithms leadig to efficiet implemetatios of modular adders (Sectio 2) ad multipliers (Sectio 3) o Virte-E ad Virte-II devices. Virte-E ad Virte-II CLBs provide fuctioal elemets for schroous ad combiatorial logic. Each CLB icludes respectivel two (Virte-E) or four (Virte-II) slices cotaiig basicall two 4-iput look-up tables (LUT), two storage elemets, ad fast carr logic dedicated to additio ad subtractio. Furthermore, Virte-E FPGAs icorporate large memor blocks orgaized i colums. Each block is a full schroous dualported 496-bit RAM whose data width ca be cofigured (, 2, 4, 8 or 6 bits). A Virte-II device embeds ma 8-bit 8-bit multipliers supportig two idepedet damic data iput ports: 8-bit siged or 7-bit usiged. 8-Kbit true dual-port RAM blocks (called block SelectRAM resources) acceptig various data/address aspect ratios are also available. Arithmetic operators dedicated to FPGAs should therefore ivolve such buildig blocks. 2 Modular Additio The modulo m additio of two umbers ad belogig to,...,m } is defied b: + if + <m, ( + ) mod m () + m if + m, ad ca be straightforwardl implemeted b a adder, a comparator, ad a subtracter. The compariso is however epesive, both i terms of area ad dela. The algorithms studied i this sectio allow to get rid of it ad lead to more efficiet hardware operators. I this paper, k log 2 m +deotes the umber of bits which are required to ecode both iputs ad output of a modulo m arithmetic operator. There are basicall three methodologies to carr out a modulo m additio [3]: Table-Based Operators. This solutio cosists i storig i a table the values ( + ) mod m for each /3/$7. (C) 23 IEEE
2 pair of iputs ad (Figure a). Its mai drawback lies i the epoetial growth of the required memor size (k 2 2k bits). Hbrid Operators. Figure b describes a modulo m adder ivolvig a stadard biar adder followed b a which corrects the sum. This architecture reduces the memor requiremets from k 2 2k bits to k 2 k+ bits. Adder-Based Operators. Aother wa to implemet Equatio () is described b Algorithm ad leads to the circuit of Figure c. Referece [3] provides for istace a proof a correctess of this method. This architecture requires ol two carr-propagate adders ad a multipleer ad is therefore well suited for FPGAs. Algorithm Modulo m additio. : Choose j such that 2 j <m<2 j 2: s + 3: s (s mod 2 j )+2 j m 4: if the carr-out bit of s or s is oe the 5: ( + ) mod m s mod 2 j 6: else 7: ( + ) mod m s mod 2 j 8: ed if 2. Modulo (2 ± ) Additio Some improvemets of the adder-based operator previousl described are possible for specific values of m. For istace, modulo (2 ) additio, or oe s complemet additio, is defied b []: ( + ) mod (2 ) ( + +)mod 2 if + + 2, + if + +< 2. Figure d depicts the architecture of the correspodig hardware operator. Due to the coditio + + 2, we perform two additios i parallel ad select the correct result with a multipleer. Remember that zero has a double represetatio i oe s complemet, amel... ad... (i.e. is cogruet to 2 (modulo 2 )). If the computatio path accommodates the secod ecodig of zero, Equatio (2) ca be rewritte as follows: ( + ) mod (2 ) ( + +)mod 2 if + 2, + if + <2. (2) (3) Note that the carr-out c out from the sum + idicates whether the icremetatio must be performed. It is still possible to evaluate + ad + +i parallel, ad to choose the correct result accordig to c out (Figure e). A alterate architecture, illustrated o Figure f, simpl adds c out to the +. Desigig a modulo (2 +)adder is a little bit trickier. Such a operator is however useful i a wider rage of applicatio icludig for istace the modulo (2 +) multiplier of the IDEA block cipher [8]. This arithmetic operatio is ofte performed i the dimiished-oe umber sstem, where a umber is represeted b ad the umber is ot used or treated as a special case []: ( + +)mod (2 +) + if + 2, ( + +)mod 2 if + < 2. ( + + c out ) mod 2. (4) Figure g ad Figure h depict two hardware operators performig the modulo (2 +)additio accordig to this algorithm. The priciple of these architectures is the same as for the modulo (2 ) adder. Let us stud the modulo (2 +)additio of two umbers i ormal represetatio. The algorithms described i this paper returs the desired result icreased b oe. Nevertheless, this propert facilitates the desig of the circuit ad ca be dealt with i ma applicatios. The modulo (2 +)additio is ow defied b: ( + +)mod (2 +) 2 if 2 ad 2, ( + ) mod 2 + c out if + <2 + (5). Two direct implemetatios of Equatio (5) are illustrated b Figure i ad Figure j [5]. Their mai drawback lies i the multipleer hadlig the special case where both operads are equal to 2. We suggest here a alterative architecture suppressig the multipleer. Let us defie the ( +2)-bit iteger s s + s...s +. The modulo (2 +)additio ca be epressed as: ( + +)mod (2 +) ( + ) mod 2 + s s + s. (6) A proof of correctess of this algorithm is provided i Ae A. Figure k depicts the resultig hardware operator which requires ol two carr-propagate adders ad a NOR gate. O Virte-E or Virte-II devices, this logic gate is implemeted withi the carr chai ad the modulo (2 +) adder fits ito a sigle CLB colum. Note that this operator also deals with umbers i dimiished-oe represetatio, /3/$7. (C) 23 IEEE
3 Optioal pipelie stage Sigle represetatio of zero Double represetatio of zero (+) mod m (a) Table based operator (+) mod m (b) Hbrid operator Modulo (2 +) operators (dimiished oe umber sstem) (+) mod m k 2 m (c) Adder based operator (+) mod m Modulo (2 +) operators (umbers i ormal represetatio) (+) mod m (d) (e) (f) Modulo (2 ) operators (+) mod m ( + +) mod m (g) ( + +) mod m (h) Most sigificat bit 2 or (i) bits + bits + bits + bits (++) mod m + bits Most sigificat bit + bits bits 2 + bits + bits (++) mod m (j) + bits bits + bits + bits (++) mod m (k) Figure. Several architectures of modulo m adders. while elimiatig the costrait,. The coversio from ormal represetatio to dimiished-oe umber sstem is ow defied b ξ ( ) mod (2 +): the umber ( ) is cogruet to 2 (modulo (2 +)). 2.2 Implemetatio Results We have writte a C program which geerates the sthesizable VHDL code of each circuit illustrated o Figure. Three parameters allow to choose oe of the modulo adders, to specif the modulus m, ad to isert a optioal pipelie stage. We have the coducted a series of eperimets with this tool i order to evaluate the area ad the dela of each modular adder accordig to m. Our first eperimet aims to compare four architectures of a modulo (2 ) adder (Table ). The operators de- All eperimets described i this paper were performed o a Su Microsstems Ultra- workstatio (44 MHz, GB of memor). All iput ad output sigals were routed through the D-tpe flip-flops available i the Iput/Output blocks of Virte-E or Virte-II devices. The optioal pipelie stage has ot bee used. The automaticall geerated VHDL code was sthesized usig Splif Pro 7..3 ad implemeted o Virte-E ad Virte-II devices emploig Xili Alliace Series 4..3i. No specific costraits were give to the sthesis tools ad it should be therefore possible to improve the results. picted b Figure d ad Figure e do ot sigificatl improve the adder-based operator defied b Algorithm. The last modulo (2 ) adder described i this paper (Figure f) does ot require a multipleer ad is therefore smaller. The dela of the four circuits is comparable. This eperimet illustrates that a peculiar umber ecodig (i.e. the double represetatio of zero) ca sometimes lead to a better hardware implemetatio of a arithmetic operator. Table 2 describes the mai specificities of some modulo (2 +)adders o a Virte-E device. Due to the required memor size, the hbrid operator (Figure b) is rather uattractive ad is limited to small moduli ( 8). Note that the table-based method works ol if 5. For 4, the operator requires for istace two 496-bit RAM blocks ad four slices, ad its dela is equal to 4.3 s. For 7, 529 slices are eeded ad the dela is the equal to 44.5 s. This eperimet also shows that our ew modulo (2 +)additio algorithm leads to the smallest circuits. 3 Modular Multiplicatio A basic modulo m multiplicatio algorithm cosists i computig w, where, < m, ad dividig this product b m. Sice divisio is hard to perform, several /3/$7. (C) 23 IEEE
4 Table. Compariso of some modulo (2 ) adders o a XCV5E-6 device Fig. c Fig. d Fig. e Fig. f 6 slices 3 slices 9 slices 25 slices 3 slices 37 slices 43 slices 49 slices 9.4 s.5 s 2.3 s 3.4 s 3.7 s 4.3 s 4.5 s 4.9 s 6 slices 2 slices 8 slices 24 slices 3 slices 36 slices 42 slices 48 slices 8. s 9. s 9.4 s.2 s.9 s. s 2.6 s 3.3 s 6 slices 2 slices 8 slices 24 slices 3 slices 36 slices 42 slices 48 slices 8. s 8.6 s 9.4 s 9.7 s.9 s.5 s 2.3 s 3. s 5 slices 8 slices 2 slices 6 slices 2 slices 24 slices 28 slices 32 slices 8.4 s 8.8 s 9.4 s.7 s 4.8 s 3.7 s 5.5 s 4.2 s Table 2. Compariso of some modulo (2 + ) adders o a XCV5E-6 device Fig. b Fig. c Fig. j Fig. k slices 2 slices.2 s 2.5 s 7 slices 5 slices 2 slices 27 slices 33 slices 39 slices 45 slices 5 slices 9.4 s.8 s 2.2 s 3. s 3.3 s 3.6 s 4.3 s 6.9 s 6 slices 3 slices 9 slices 25 slices 3 slices 37 slices 43 slices 49 slices 8.7 s.6 s 2.2 s 3.6 s 4.4 s 4.9 s 5.7 s 8.7 s 6 slices slices 5 slices 9 slices 23 slices 27 slices 3 slices 35 slices 7.8 s.6 s.6 s 3.4 s 4.5 s 3.8 s 4.7 s 9.2 s algorithms have bee proposed to overcome this problem. Referece [6] provides a good bibliograph o this subject. All these solutios are however dedicated to VLSI implemetatios; cosequetl, we propose here a stud of some modular multipliers based o the buildig blocks available i recet FPGAs. Aalogousl to additio, modulo m multiplicatio ca be implemeted b meas of tables (Figure 2a). This approach is however limited to small moduli due to the epoetial growth of the required memor, ad other architectures must be ivestigated. 3. Multiplicatio with Subsequet Modulo Correctio This modulo m multiplicatio scheme is dedicated to FPGAs embeddig small multipliers ad memor blocks. The priciple cosists i computig the 2k-bit wide product ad the performig a modulo correctio b meas of a table ad a modulo m additio. Give a umber 2 j, the algorithm is described as follows: () mod m (() mod 2 j +2 j () div 2 j ) mod m (() mod 2 j +( (m 2 j ) () div 2 j ) mod m) mod m if m>2 j, (() mod 2 j + ((2 j (7) m) () div 2 j ) mod m) mod m if m<2 j. The case where m 2 j is straightforward ad will ot be addressed i this paper. This scheme requires a usiged multiplier, a memor to store all possible values of ( (m 2 j ) () div 2 j ) mod m or ((2 j m) () div 2 j ) mod m, ad a modulo m adder. Let us defie p () mod 2 j ad p ( (m 2 j ) () div 2 j ) mod m (or p ((2 j m) () div 2 j ) mod m). We have ow to distiguish the two followig cases: For m>2 j, p,p m ad we deduce that p +p 2m 2. The fial additio ca therefore be performed with the modulo m adder described i sectio 2 (Figure 2b). For m<2 j,wehave p < 2 j, p <m, ad p + p 2 j + m 2. The architecture of the modulo m multiplier depeds o 2 j + m 2. If this value is strictl smaller tha 2m, the operator is defied b: () mod m p + p if p + p <m, (8) p + p m if m p + p < 2m. From 2 j + m 2 < 2m, we deduce that 2 j m +. Sice m<2 j, Equatio (8) holds iff 2 j m +. For other values of 2 j, the modulo m multiplicatio is formulated as: () mod m p + p if p + p <m, p + p m if m p + p < 2m, p + p 2m if p + p 2m /3/$7. (C) 23 IEEE
5 Figure 2c illustrates the correspodig hardware operator. 3.2 Modulo (2 + ) Multiplicatio Modulo (2 +)multiplicatio ca be performed accordig to Equatio (7). If the target FPGA does ot embed small multipliers, the implemetatio of this scheme is however epesive. We propose a alterate architecture based o the algorithm described b Ma i [9]. Assume that ψ ψ...ψ is the dimiished-oe represetatio of, i.e. ψ ( ) mod (2 +). Whe is eve, Ma has proved that: mod (2 +) ( 2 ) P i + mod (2 +), (9) 2 i where P i 2 2i ( 2ψ 2i + ψ 2i+ + ψ 2i ) ad ψ ( ψ ψ ) mod (2 +). Each partial product P i ca be easil computed from the dimiished-oe represetatio of. Whe is odd, the product mod (2 +)is give b: mod (2 +) P 2 ( }} ( 2 (ψ + ψ 2 ) ) + +(( )/2+) ) 2 i P i mod (2 +), () where ψ ψ mod (2 +). Ma computes the sum of the partial products ad the costat with a carr-save adder, the performs a modulo (2 +)reductio with two modulo (2 +)carr-save adders ad oe modulo (2 +)carr-propagate adder [9]. This architecture does ot take advatage of the fast carr logic available i FPGAs ad we suggest here a implemetatio of Equatios (9) ad () based o our ew modulo (2 +)adder described i Sectio 2. Both equatios impl to sum up /2 partial products P i ad the costat /2. Remember that our modulo (2 +)adder returs the sum of its two operads icreased b oe. Cosequetl, if we compute the sum /2 i P i with ( /2 ) such adders, we obtai ( /2 i P i + /2 ) mod (2 +), which is the dimiished-oe represetatio of the product. Figure 3a depicts the correspodig hardware operator which takes as iputs the dimiished-oe represetatios of ad, ad returs ( ) mod (2 +). Sice ( +(2 ) + ) mod (2 +) ( ) mod (2 +), the coversio from usiged iteger to dimiished-oe umber sstem ca be achieved with our modulo (2 +)adder. The iverse coversio is performed with a carr-propagate adder (Figure 3a): it is eas to verif that (a +)mod (2 +) i a i2 i +ā whe a,...,2 }. Let us cosider the multiplicatio i Z 2 + a Z 2 + gcd(a, 2 +) } (i.e. the multiplicative group of Z 2 +). Sice (Z 2 +, ) is a group, we kow that () mod (2 +) ad it is therefore possible to represet the umber 2 b. This trick saves oe bit ad allows two improvemets of the multiplier based o Ma s algorithm: Due to the special ecodig of 2, the dimiishedoe represetatio of a umber Z 2 + is ( ) mod 2. We obtai for istace ( ) mod 2 2, which is the dimiished-oe represetatio of 2. It is eas to check that ( ) mod (2 +) ( ) mod 2 whe 2. The coversio from dimiished-oe umber sstem to usiged iteger does ot require a additioal stage amore (Figure 3b). It is ideed possible to modif the last adder of the tree i order to compute (a + b + 2) mod (2 +)accordig to: (a + b +2)mod (2 +) ( ) s i 2 i + s + s mod 2, () i where s s + s...s a + b +. The proof of correctess of this algorithm is straightforward. Multiplicatio i Z is for istace the critical operatio of the IDEA block cipher [8]. Several modulo (2 +) multipliers have cosequetl bee ivestigated over the past ears (see for istace [, 4, ]). Aother implemetatio of Ma s algorithm has bee proposed b Hämäläie et al. i [5]. This architecture is also based o carr-propagate adders. However, modulo (2 +)additios are carried out b the circuit of Figure j, ad a additioal stage performs the coversio. This modular multiplier is therefore larger ad slower tha ours. Aother wa to implemet Equatio (9) or Equatio () cosists i computig the sum s /2 i P i + /2 with a carr-propagate adder tree, the i performig a modulo (2 +)correctio. We assume that is eve ad defie s s mod 2 ad s s div 2. Sice s 2 ad s /2, we obtai: s mod (2 +)(s +2 s ) mod (2 +) (s s ) mod (2 +) (s +2 s +)mod (2 +) (s + s +2)mod (2 +) s + s +2 if s + s +< 2, s + s + 2 if s + s + 2, /3/$7. (C) 23 IEEE
6 (*) mod m p p Modulo m adder k 2 m (*) mod m p p Modulo m adder 2m m (*) mod m (a) Table based operator (b) Multiplicatio with subsequet modulo correctio j (m>2 ) (c) Multiplicatio with subsequet modulo correctio j (m<2 ) Figure 2. Three architectures of modulo m multipliers. (a+b+) mod (2 +) ( )mod(2 +) Partial Product Geeratio ( )mod(2 +) (Σ P + /2 ) mod (2 +) i (a) Dimiished oe umber sstem a a + bits a... a + bits (a+)mod(2 +) Coversio from dimiished oe represetatio to ormal represetatio a b + bits bits bits (a+b+2) mod (2 +) ( )mod 2 Partial Product Geeratio (Σ i P + /2) mod (2 +) (b) Multiplicatio i Z * 2 + ( )mod 2 Optioal pipelie stage Figure 3. Architectures of a modulo (2 + ) multiplier based o Ma s algorithm. which is the dimiished-oe represetatio of () mod (2 +). Figure 4a depicts the correspodig hardware operator. Small improvemets are agai possible whe, Z 2 +. The coversio from ormal represetatio to the dimiished-oe umber sstem is eactl the same as for the operator based o modulo (2 +)adders (Figure 3b). Note fiall that s mod (2 +) 2. Due to the special ecodig of zero, () mod (2 +)(smod (2 +)+)mod 2 ad we perform the coversio b settig the iput carr of the fial adder to oe (Figure 4b). 3.3 Implemetatio Results This sectio describes the mai characteristics of some modulo m multipliers studied i this paper. The eperimetal setup is the same as for modular adders. Table 3 digests the mai characteristics of modulo m multipliers based o a multiplicatio with subsequet modulo correctio for Virte-II devices. We ol cosider here operators requirig a sigle 8-Kbit memor block, which defies the maimum value for m. Remember that k log 2 m + deotes the umber of bits required to ecode m. Whe m 2 k, Equatio (7) ields: () mod m (() mod 2 k + ((2 k m) () div 2 k ) mod m. The table is addressed b the k-bit word () div 2 k ad also returs a k-bit umber. Cosequetl, the block SelectRAM is cofigured i the K 8-bit mode (i.e address bits ad 8 data bits) ad the modulus m is comprised betwee 3 ad 23. Table 4 summarizes the area ad the dela of several modulo (2 +)multipliers whe, Z 2 +. I this eperimet, we compare the two architectures discussed i this paper (Figures 3b ad 4b) to a operator based o the modified Low-High algorithm proposed i []. This circuit ivolves a usiged multiplier, a multipleer to hadle the special cases where or, ad a modulo correctio (Figure 4c). Our eperimets illustrate that: The architecture based o a carr-propagate adder tree ad a modulo (2 +) correctio seems to be the better implemetatio of Ma s algorithm for FPGAs. This result is ot surprisig: ote that our modulo (2 + ) adder is roughl twice as large as a ( +)-bit carr-propagate adder. Cosequetl, the two modulo (2 +)multipliers previousl described respectivel /3/$7. (C) 23 IEEE
7 ( )mod(2 +) ( )mod(2 +) ( )mod 2 ( )mod 2 Usiged multiplier Carr propagate adders (Σ Partial Product Geeratio s s P + /2 mod (2 +) i (a) Dimiished oe umber sstem ) Modulo (2 +) correctio Partial Product Geeratio s s (Σ P + /2) mod (2 +) i * (b) Multiplicatio i Z 2 + Σ P + /2 i & "..."! most sig ificat bits carr out & "..."! bits () mod (2 +)!! least sig ificat bits (c) Modified Low High algorithm Figure 4. Two other architectures of a modulo (2 + ) multiplier based o Ma s algorithm ad the architecture based o the modified Low-High algorithm described i []. require 2 /2 (Figure 3b) ad /2 +2(Figure 4b) carr-propagate adders to sum the partial products. The modified Low-High algorithm leads to smaller circuits whe the modulo (2 +)multiplier is purel combiatorial. The -bit -bit usiged multiplier sums the partial products P i 2 i i, i,..., } with a tree of carr-propagate adders. This architecture takes advatage of the dedicated AND gate associated with each LUT i order to geerate the partial products. Although Ma s algorithm reduces the amout of partial products, their geeratio ivolves much more hardware resources (LUTs ad multipleers). However, whe pipelie stages are iserted to reduce the dela, the circuit illustrated o Figure 4b is attractive for 28. This result is eplaied b the fact that pipeliig the usiged multiplier of the operator based o the modified Low-High algorithm is epesive. 4 Coclusio We have described ad compared several modular adders ad multipliers ivolvig various buildig blocks (carrpropagate adders, tables, ad small multipliers). Our mai results iclude the desig of a ew modulo (2 +)adder, a modulo m multiplier based o the embedded multipliers ad memor blocks available i Virte-II devices, ad implemetatios of Ma s algorithm carefull optimized for FPGAs. Our eperimets idicate that the choice of a operator depeds o several parameters such as the modulus m, the target FPGA famil, ad the umber of iteral pipelie stages. However, our VHDL geerators allow to quickl eplore a wide parameter space ad to determie which architecture is most appropriate for a give applicatio. Ackowledgmets The author would like to thak the Miistère Fraçais de la Recherche (grat # 48 CDR ACI jeues chercheurs ), the Swiss Natioal Sciece Foudatio, ad the Xili Uiversit Program for their support. A Proof of the New Modulo (2 + ) Additio Algorithm Let us demostrate that the algorithm defied b Equatio (6) carries out ( + +)mod (2 +)whe, 2. First of all, let us ote that ad ( + +)mod (2 + + if + <2, +) + 2 if /3/$7. (C) 23 IEEE
8 Table 3. Multiplicatio with subsequet modulo correctio o a XC2V4-6 device. Each operator requires a small multiplier ad a sigle 8-Kbit memor block. m 5 m 3 m 29 m 6 m 25 m 253 m 59 m 2 Area [slices] Dela [s] Table 4. Modulo (2 + ) multiplicatio i Z 2 + o a XCV2E-6 device Figure 3b 4 slices 6 slices 4 slices 254 slices 398 slices 575 slices 885 slices 56 slices (without pipelie).6 s 2.5 s 3.9 s 35.5 s 47.3 s 5.8 s 56.6 s 55.8 s Figure 3b 5 slices 66 slices 56 slices 264 slices 433 slices 63 slices 4 slices 3 slices (with pipelie) 6.7 s 8.9 s 9.7 s.8 s 3.3 s 2.4 s 5. s 5. s Figure 4b 5 slices 57 slices 23 slices 22 slices 325 slices 46 slices 725 slices 939 slices (without pipelie).2 s 8.8 s 24. s 28.7 s 34.8 s 35.9 s 39. s 42.6 s Figure 4b 8 slices 63 slices 38 slices 223 slices 362 slices 494 slices 856 slices 89 slices (with pipelie) 5.8 s 8.5 s 9.9 s.6 s.9 s.5 s 2. s 3.2 s Figure 4c 9 slices 53 slices slices 82 slices 27 slices 372 slices 492 slices 629 slices (without pipelie) 6. s 2.8 s 27.6 s 3. s 34.5 s 37.9 s 39.3 s 44.2 s Figure 4c 25 slices 77 slices 39 slices 22 slices 353 slices 46 slices 592 slices 743 slices (with pipelie) 7. s 9.4 s.4 s 2.6 s 2.8 s 4. s 3.5 s 5.9 s We have to distiguish the three followig cases to establish the correctess of our algorithm: For (i.e. 2 ), we have ( + ) mod 2, s, ad s +. Our algorithm returs ( + +)mod (2 +)2 + 2, which is the correct result. For 2 + <2 +, we kow that s + ad s. Cosequetl, ( + +)mod (2 +) ( + ) mod Fiall, for + <2, s + s ad ( + ) mod 2 +. We obtai ( + +)mod (2 + ) + +. Refereces [] J.-L. Beuchat. Modular Multiplicatio for FPGA Implemetatio of the IDEA Block Cipher. Techical Report 22-32, Laboratoire de l Iformatique du Parallélisme, Ecole Normale Supérieure de Lo, 46 Allée d Italie, Lo Cede 7, Sept. 22. [2] J.-L. Beuchat ad A. Tisserad. Small Multiplier-based Multiplicatio ad Divisio Operators for Virte-II Devices. I M. Gleser, P. Zipf, ad M. Reovell, editors, Field- Programmable Logic ad Applicatios Recofigurable Computig Is Goig Maistream, umber 2438 i Lecture Notes i Computer Sciece, pages Spriger, 22. [3] A. V. Curiger. VLSI Architectures for Computatios i Fiite Rigs ad Fields, volume 26 of Series i Microelectroics. Hartug-Gorre Verlag, 993. [4] A. V. Curiger, H. Boeberg, ad H. Kaesli. Regular VLSI Architectures for Multiplicatio Modulo (2 +). IEEE Joural of Solid-State Circuits, 26(7):99 994, 99. [5] A. Hämäläie, M. Tommiska, ad J. Skttä Gigabits per Secod implemetatio of the IDEA Crptographic Algorithm. I M. Gleser, P. Zipf, ad M. Reovell, editors, Field-Programmable Logic ad Applicatios Recofigurable Computig Is Goig Maistream, umber 2438 i Lecture Notes i Computer Sciece, pages Spriger, 22. [6] A. A. Hiasat. New Efficiet Structures for a Modular Multiplier for RNS. IEEE Trasactios o Computers, 49(2):7 74, 2. [7] A. A. Hiasat. High-Speed ad Reduced-Area Modular Adder Structures for RNS. IEEE Trasactios o Computers, 5():84 89, 22. [8] X. Lai. O the Desig ad Securit of Block Ciphers. ETH Series i Iformatio Processig. Hartug Gorre Verlag Kostaz, 992. [9] Y. Ma. A Simplified Architecture for Modulo (2 +)Multiplicatio. IEEE Trasactios o Computers, 47(3): , 998. [] R. Zimmerma. Efficiet VLSI Implemetatio of Modulo (2 ± ) Additio ad Multiplicatio. I Proceedigs of the 4th IEEE Smposium o Computer Arithmetic, pages 58 67, Adelaide, Australia, April /3/$7. (C) 23 IEEE
High Speed Area Efficient Modulo 2 1
High Speed Area Efficiet Modulo 2 1 1-Soali Sigh (PG Scholar VLSI, RKDF Ist Bhopal M.P) 2- Mr. Maish Trivedi (HOD EC Departmet, RKDF Ist Bhopal M.P) Adder Abstract Modular adder is oe of the key compoets
More informationOPTIMIZATION OF RNS FIR FILTERS FOR 6-INPUTS LUT BASED FPGAS
OPTIMIZATION OF RNS FIR FILTERS FOR 6-INPUTS LUT BASED FPGAS G.C. Cardarilli, M. Re, A. Salsao Uiversity of Rome Tor Vergata Departmet of Electroic Egieerig Via del Politecico 1 / 00133 / Rome / ITAL {marco.re,
More informationReducing Power Dissipation in Complex Digital Filters by using the Quadratic Residue Number System Λ
Reducig Power Dissipatio i Complex Digital Filters by usig the Quadratic Residue Number System Λ Agelo D Amora, Alberto Naarelli, Marco Re ad Gia Carlo Cardarilli Departmet of Electrical Egieerig Uiversity
More informationLogarithms APPENDIX IV. 265 Appendix
APPENDIX IV Logarithms Sometimes, a umerical expressio may ivolve multiplicatio, divisio or ratioal powers of large umbers. For such calculatios, logarithms are very useful. They help us i makig difficult
More informationCHAPTER 5 A NEAR-LOSSLESS RUN-LENGTH CODER
95 CHAPTER 5 A NEAR-LOSSLESS RUN-LENGTH CODER 5.1 GENERAL Ru-legth codig is a lossless image compressio techique, which produces modest compressio ratios. Oe way of icreasig the compressio ratio of a ru-legth
More informationELEC 204 Digital Systems Design
Fall 2013, Koç Uiversity ELEC 204 Digital Systems Desig Egi Erzi College of Egieerig Koç Uiversity,Istabul,Turkey eerzi@ku.edu.tr KU College of Egieerig Elec 204: Digital Systems Desig 1 Today: Datapaths
More informationA Comparative Study on LUT and Accumulator Radix-4 Based Multichannel RNS FIR Filter Architectures
A Comparative Study o LUT ad Accumulator Radix-4 Based Multichael RNS FIR Filter Architectures Britto Pari. J #, Joy Vasatha Rai S.P *2 # Research Scholar, Departmet of Electroics Egieerig, MIT campus,
More informationA Comparison on FPGA of Modular Multipliers Suitable for Elliptic Curve Cryptography over GF(p) for Specific p Values
A Compariso o FPGA of Modular Multipliers Suitable for Elliptic Curve Cryptography over GF(p) for Specific p Values Mark Hamilto, William Marae, Araud Tisserad To cite this versio: Mark Hamilto, William
More informationModulo 2 n +1 Arithmetic Units with Embedded Diminished-to-Normal Conversion
2011 14th Euromicro Coferece o Digital System Desig Modulo 2 +1 Arithmetic Uits with Embedded Dimiished-to-Normal Coversio Evagelos Vassalos, Dimitris Bakalis Electroics Laboratory, Dept. of Physics Uiversity
More informationDesign of FPGA- Based SPWM Single Phase Full-Bridge Inverter
Desig of FPGA- Based SPWM Sigle Phase Full-Bridge Iverter Afarulrazi Abu Bakar 1, *,Md Zarafi Ahmad 1 ad Farrah Salwai Abdullah 1 1 Faculty of Electrical ad Electroic Egieerig, UTHM *Email:afarul@uthm.edu.my
More informationA study on the efficient compression algorithm of the voice/data integrated multiplexer
A study o the efficiet compressio algorithm of the voice/data itegrated multiplexer Gyou-Yo CHO' ad Dog-Ho CHO' * Dept. of Computer Egieerig. KyiigHee Uiv. Kiheugup Yogiku Kyuggido, KOREA 449-71 PHONE
More informationIntermediate Information Structures
Modified from Maria s lectures CPSC 335 Itermediate Iformatio Structures LECTURE 11 Compressio ad Huffma Codig Jo Roke Computer Sciece Uiversity of Calgary Caada Lecture Overview Codes ad Optimal Codes
More informationApplication of Improved Genetic Algorithm to Two-side Assembly Line Balancing
206 3 rd Iteratioal Coferece o Mechaical, Idustrial, ad Maufacturig Egieerig (MIME 206) ISBN: 978--60595-33-7 Applicatio of Improved Geetic Algorithm to Two-side Assembly Lie Balacig Ximi Zhag, Qia Wag,
More informationReconfigurable architecture of RNS based high speed FIR filter
Idia Joural of Egieerig & Materials Scieces Vol. 21, April 214, pp. 233-24 Recofigurable architecture of RNS based high speed FIR filter J Britto Pari* & S P Joy Vasatha Rai Departmet of Electroics Egieerig,
More informationA New Space-Repetition Code Based on One Bit Feedback Compared to Alamouti Space-Time Code
Proceedigs of the 4th WSEAS It. Coferece o Electromagetics, Wireless ad Optical Commuicatios, Veice, Italy, November 0-, 006 107 A New Space-Repetitio Code Based o Oe Bit Feedback Compared to Alamouti
More informationx y z HD(x, y) + HD(y, z) HD(x, z)
Massachusetts Istitute of Techology Departmet of Electrical Egieerig ad Computer Sciece 6.02 Solutios to Chapter 5 Updated: February 16, 2012 Please sed iformatio about errors or omissios to hari; questios
More informationA Novel Three Value Logic for Computing Purposes
Iteratioal Joural o Iormatio ad Electroics Egieerig, Vol. 3, No. 4, July 23 A Novel Three Value Logic or Computig Purposes Ali Soltai ad Saeed Mohammadi Abstract The aim o this article is to suggest a
More informationDesign of FPGA Based SPWM Single Phase Inverter
Proceedigs of MUCEET2009 Malaysia Techical Uiversities Coferece o Egieerig ad Techology Jue 20-22, 2009, MS Garde,Kuata, Pahag, Malaysia MUCEET2009 Desig of FPGA Based SPWM Sigle Phase Iverter Afarulrazi
More informationCHAPTER 6 IMPLEMENTATION OF DIGITAL FIR FILTER
CHAPTER 6 IMPLEMENTATION OF DIGITAL FIR FILTER 6.1 INTRODUCTION The digital FIR filters are commo compoets i may digital sigal processig (DSP) systems. There are various applicatios like high speed/low
More informationINCREASE OF STRAIN GAGE OUTPUT VOLTAGE SIGNALS ACCURACY USING VIRTUAL INSTRUMENT WITH HARMONIC EXCITATION
XIX IMEKO World Cogress Fudametal ad Applied Metrology September 6, 9, Lisbo, Portugal INCREASE OF STRAIN GAGE OUTPUT VOLTAGE SIGNALS ACCURACY USING VIRTUAL INSTRUMENT WITH HARMONIC EXCITATION Dalibor
More informationCOMPRESSION OF TRANSMULTIPLEXED ACOUSTIC SIGNALS
COMPRESSION OF TRANSMULTIPLEXED ACOUSTIC SIGNALS Mariusz Ziółko, Przemysław Sypka ad Bartosz Ziółko Departmet of Electroics, AGH Uiversity of Sciece ad Techology, al. Mickiewicza 3, 3-59 Kraków, Polad,
More informationSurvey of Low Power Techniques for ROMs
Survey of Low Power Techiques for ROMs Edwi de Agel Crystal Semicoductor Corporatio P.O Box 17847 Austi, TX 78744 Earl E. Swartzlader, Jr. Departmet of Electrical ad Computer Egieerig Uiversity of Texas
More informationHigh-Order CCII-Based Mixed-Mode Universal Filter
High-Order CCII-Based Mixed-Mode Uiversal Filter Che-Nog Lee Departmet of Computer ad Commuicatio Egieerig, Taipei Chegshih Uiversity of Sciece ad Techology, Taipei, Taiwa, R. O. C. Abstract This paper
More informationCross-Layer Performance of a Distributed Real-Time MAC Protocol Supporting Variable Bit Rate Multiclass Services in WPANs
Cross-Layer Performace of a Distributed Real-Time MAC Protocol Supportig Variable Bit Rate Multiclass Services i WPANs David Tug Chog Wog, Jo W. Ma, ad ee Chaig Chua 3 Istitute for Ifocomm Research, Heg
More informationX-Bar and S-Squared Charts
STATGRAPHICS Rev. 7/4/009 X-Bar ad S-Squared Charts Summary The X-Bar ad S-Squared Charts procedure creates cotrol charts for a sigle umeric variable where the data have bee collected i subgroups. It creates
More informationLossless image compression Using Hashing (using collision resolution) Amritpal Singh 1 and Rachna rajpoot 2
Lossless image compressio Usig Hashig (usig collisio resolutio) Amritpal Sigh 1 ad Racha rajpoot 2 1 M.Tech.* CSE Departmet, 2 Departmet of iformatio techology Guru Kashi UiversityTalwadi Sabo, Bathida
More informationPermutation Enumeration
RMT 2012 Power Roud Rubric February 18, 2012 Permutatio Eumeratio 1 (a List all permutatios of {1, 2, 3} (b Give a expressio for the umber of permutatios of {1, 2, 3,, } i terms of Compute the umber for
More informationA SIMPLE METHOD OF GOAL DIRECTED LOSSY SYNTHESIS AND NETWORK OPTIMIZATION
A SIMPL MOD OF GOAL DIRCD LOSSY SYNSIS AND NWORK OPIMIZAION Karel ájek a), ratislav Michal, Jiří Sedláček a) Uiversity of Defece, Kouicova 65,63 00 Bro,Czech Republic, Bro Uiversity of echology, Kolejí
More informationHDL LIBRARY OF PROCESSING UNITS FOR GENERIC AND DVB-S2 LDPC DECODING
HDL LIBRARY OF PROCESSING UNITS FOR GENERIC AND DVB-S2 LDPC DECODING Marco Gomes 1,2, Gabriel Falcão 1,2, João Goçalves 1,2, Vitor Silva 1,2, Miguel Falcão 3, Pedro Faia 2 1 Istitute of Telecommuicatios,
More informationA SIMPLE METHOD OF GOAL DIRECTED LOSSY SYNTHESIS AND NETWORK OPTIMIZATION
49 A SIMPL MOD OF GOAL DIRCD LOSSY SYNSIS AND NWORK OPIMIZAION K. ájek a),. Michal b), J. Sedláek b), M. Steibauer b) a) Uiversity of Defece, Kouicova 65,63 00 ro,czech Republic, b) ro Uiversity of echology,
More informationRun-Time Error Detection in Polynomial Basis Multiplication Using Linear Codes
Ru-Time Error Detectio i Polyomial Basis Multiplicatio Usig Liear Codes Siavash Bayat-Saramdi ad M.A. Hasa Departmet of Electrical ad Computer Egieerig, Uiversity of Waterloo Waterloo, Otario, Caada N2L
More informationFPGA Implementation of the Ternary Pulse Compression Sequences
FPGA Implemetatio of the Terary Pulse Compressio Sequeces N.Balaji 1, M. Sriivasa rao, K.Subba Rao 3, S.P.Sigh 4 ad N. Madhusudhaa Reddy 4 Abstract Terary codes have bee widely used i radar ad commuicatio
More informationDesign of Area and Speed Efficient Modulo 2 n -1 Multiplier for Cryptographic Applications
Iteratioal Joural of Sciece, Egieerig ad Techology Research (IJSETR) Desig of Area ad Speed Efficiet Modulo 2-1 Multiplier for Cryptographic Applicatios Abstract The ecryptio ad decryptio of PKC algorithms
More informationTechnical Explanation for Counters
Techical Explaatio for ers CSM_er_TG_E Itroductio What Is a er? A er is a device that couts the umber of objects or the umber of operatios. It is called a er because it couts the umber of ON/OFF sigals
More informationOn Parity based Divide and Conquer Recursive Functions
O Parity based Divide ad Coquer Recursive Fuctios Sug-Hyu Cha Abstract The parity based divide ad coquer recursio trees are itroduced where the sizes of the tree do ot grow mootoically as grows. These
More informationMassachusetts Institute of Technology Dept. of Electrical Engineering and Computer Science Fall Semester, Introduction to EECS 2.
Massachusetts Istitute of Techology Dept. of Electrical Egieerig ad Computer Sciece Fall Semester, 006 6.08 Itroductio to EECS Prelab Exercises Pre-Lab#3 Modulatio, demodulatio, ad filterig are itegral
More informationPRACTICAL FILTER DESIGN & IMPLEMENTATION LAB
1 of 7 PRACTICAL FILTER DESIGN & IMPLEMENTATION LAB BEFORE YOU BEGIN PREREQUISITE LABS Itroductio to Oscilloscope Itroductio to Arbitrary/Fuctio Geerator EXPECTED KNOWLEDGE Uderstadig of LTI systems. Laplace
More informationCP 405/EC 422 MODEL TEST PAPER - 1 PULSE & DIGITAL CIRCUITS. Time: Three Hours Maximum Marks: 100
PULSE & DIGITAL CIRCUITS Time: Three Hours Maximum Marks: 0 Aswer five questios, takig ANY TWO from Group A, ay two from Group B ad all from Group C. All parts of a questio (a, b, etc. ) should be aswered
More informationPOWERS OF 3RD ORDER MAGIC SQUARES
Fuzzy Sets, Rough Sets ad Multivalued Operatios ad Applicatios, Vol. 4, No. 1, (Jauary-Jue 01): 37 43 Iteratioal Sciece Press POWERS OF 3RD ORDER MAGIC SQUARES Sreerajii K.S. 1 ad V. Madhukar Mallayya
More information8. Combinatorial Structures
Virtual Laboratories > 0. Foudatios > 1 2 3 4 5 6 7 8 9 8. Combiatorial Structures The purpose of this sectio is to study several combiatorial structures that are of basic importace i probability. Permutatios
More informationFaulty Clock Detection for Crypto Circuits Against Differential Faulty Analysis Attack
Faulty Clock Detectio for Crypto Circuits Agaist Differetial Faulty Aalysis Attack Pei uo ad Yusi Fei Departmet of Electrical ad Computer Egieerig Northeaster Uiversity, Bosto, MA 02115 Abstract. Differetial
More informationComparison of Frequency Offset Estimation Methods for OFDM Burst Transmission in the Selective Fading Channels
Compariso of Frequecy Offset Estimatio Methods for OFDM Burst Trasmissio i the Selective Fadig Chaels Zbigiew Długaszewski Istitute of Electroics ad Telecommuicatios Pozań Uiversity of Techology 60-965
More information7. Counting Measure. Definitions and Basic Properties
Virtual Laboratories > 0. Foudatios > 1 2 3 4 5 6 7 8 9 7. Coutig Measure Defiitios ad Basic Properties Suppose that S is a fiite set. If A S the the cardiality of A is the umber of elemets i A, ad is
More informationA New Design of Log-Periodic Dipole Array (LPDA) Antenna
Joural of Commuicatio Egieerig, Vol., No., Ja.-Jue 0 67 A New Desig of Log-Periodic Dipole Array (LPDA) Atea Javad Ghalibafa, Seyed Mohammad Hashemi, ad Seyed Hassa Sedighy Departmet of Electrical Egieerig,
More informationTest Time Minimization for Hybrid BIST with Test Pattern Broadcasting
Test Time Miimizatio for Hybrid BIST with Test Patter Broadcastig Raimud Ubar, Maksim Jeihhi Departmet of Computer Egieerig Talli Techical Uiversity EE-126 18 Talli, Estoia {raiub, maksim}@pld.ttu.ee Gert
More informationA SELECTIVE POINTER FORWARDING STRATEGY FOR LOCATION TRACKING IN PERSONAL COMMUNICATION SYSTEMS
A SELETIVE POINTE FOWADING STATEGY FO LOATION TAKING IN PESONAL OUNIATION SYSTES Seo G. hag ad hae Y. Lee Departmet of Idustrial Egieerig, KAIST 373-, Kusug-Dog, Taejo, Korea, 305-70 cylee@heuristic.kaist.ac.kr
More informationA New Implementation for a 2 n 1 Modular Adder Through Carbon Nanotube Field Effect Transistors
April 2015, Volume 2, Number 2 (pp. 129 139) http://www.jcomsec.org Joural of Computig ad Security A New Implemetatio for a 2 1 Modular Adder Through Carbo Naotube Field Effect Trasistors Seyyed Ashka
More informationPHY-MAC dialogue with Multi-Packet Reception
PHY-AC dialogue with ulti-packet Receptio arc Realp 1 ad Aa I. Pérez-Neira 1 CTTC-Cetre Tecològic de Telecomuicacios de Cataluya Edifici Nexus C/Gra Capità, - 0803-Barceloa (Cataluya-Spai) marc.realp@cttc.es
More informationAME50461 SERIES EMI FILTER HYBRID-HIGH RELIABILITY
PD-94595A AME5046 SERIES EMI FILTER HYBRID-HIGH RELIABILITY Descriptio The AME Series of EMI filters have bee desiged to provide full compliace with the iput lie reflected ripple curret requiremet specified
More informationThe Eye. Objectives: Introduction. PHY 192 The Eye 1
PHY 92 The Eye The Eye Objectives: Describe the basic process of image formatio by the huma eye ad how it ca be simulated i the laboratory. Kow what measuremets are ecessary to quatitatively diagose ear-sightedess
More informationCh 9 Sequences, Series, and Probability
Ch 9 Sequeces, Series, ad Probability Have you ever bee to a casio ad played blackjack? It is the oly game i the casio that you ca wi based o the Law of large umbers. I the early 1990s a group of math
More informationDelta- Sigma Modulator based Discrete Data Multiplier with Digital Output
K.Diwakar et al. / Iteratioal Joural of Egieerig ad echology (IJE Delta- Sigma Mulator based Discrete Data Multiplier with Digital Output K.Diwakar #,.ioth Kumar *2, B.Aitha #3, K.Kalaiarasa #4 # Departmet
More informationPROJECT #2 GENERIC ROBOT SIMULATOR
Uiversity of Missouri-Columbia Departmet of Electrical ad Computer Egieerig ECE 7330 Itroductio to Mechatroics ad Robotic Visio Fall, 2010 PROJECT #2 GENERIC ROBOT SIMULATOR Luis Alberto Rivera Estrada
More informationAkinwaJe, A.T., IbharaJu, F.T. and Arogundade, 0.1'. Department of Computer Sciences University of Agriculture, Abeokuta, Nigeria
COMPARATIVE ANALYSIS OF ARTIFICIAL NEURAL NETWORK'S BACK PROPAGATION ALGORITHM TO STATISTICAL LEAST SQURE METHOD IN SECURITY PREDICTION USING NIGERIAN STOCK EXCHANGE MARKET AkiwaJe, A.T., IbharaJu, F.T.
More informationDesign and Implementation of Vedic Algorithm using Reversible Logic Gates
www.ijecs.i Iteratioal Joural Of Egieerig Ad Computer Sciece ISSN: 2319-7242 Volume 4 Issue 8 Aug 2015, Page No. 13734-13738 Desig ad Implemetatio of Vedic Algorithm usig Reversible Logic s Hemagi P.Patil
More informationHybrid BIST Optimization for Core-based Systems with Test Pattern Broadcasting
Hybrid BIST Optimizatio for Core-based Systems with Test Patter Broadcastig Raimud Ubar, Masim Jeihhi Departmet of Computer Egieerig Talli Techical Uiversity, Estoia {raiub, masim}@pld.ttu.ee Gert Jerva,
More informationAPPLICATION NOTE UNDERSTANDING EFFECTIVE BITS
APPLICATION NOTE AN95091 INTRODUCTION UNDERSTANDING EFFECTIVE BITS Toy Girard, Sigatec, Desig ad Applicatios Egieer Oe criteria ofte used to evaluate a Aalog to Digital Coverter (ADC) or data acquisitio
More informationGeneral Model :Algorithms in the Real World. Applications. Block Codes
Geeral Model 5-853:Algorithms i the Real World Error Correctig Codes I Overview Hammig Codes Liear Codes 5-853 Page message (m) coder codeword (c) oisy chael decoder codeword (c ) message or error Errors
More informationSingle Bit DACs in a Nutshell. Part I DAC Basics
Sigle Bit DACs i a Nutshell Part I DAC Basics By Dave Va Ess, Pricipal Applicatio Egieer, Cypress Semicoductor May embedded applicatios require geeratig aalog outputs uder digital cotrol. It may be a DC
More informationAn Adaptive Image Denoising Method based on Thresholding
A Adaptive Image Deoisig Method based o Thresholdig HARI OM AND MANTOSH BISWAS Departmet of Computer Sciece & Egieerig Idia School of Mies, Dhabad Jharkad-86004 INDIA {hariom4idia, matoshb}@gmail.com Abstract
More information3. Error Correcting Codes
3. Error Correctig Codes Refereces V. Bhargava, Forward Error Correctio Schemes for Digital Commuicatios, IEEE Commuicatios Magazie, Vol 21 No1 11 19, Jauary 1983 Mischa Schwartz, Iformatio Trasmissio
More informationCombined Scheme for Fast PN Code Acquisition
13 th Iteratioal Coferece o AEROSPACE SCIENCES & AVIATION TECHNOLOGY, ASAT- 13, May 6 8, 009, E-Mail: asat@mtc.edu.eg Military Techical College, Kobry Elkobbah, Cairo, Egypt Tel : +(0) 4059 4036138, Fax:
More informationOptimal Arrangement of Buoys Observable by Means of Radar
Optimal Arragemet of Buoys Observable by Meas of Radar TOMASZ PRACZYK Istitute of Naval Weapo ad Computer Sciece Polish Naval Academy Śmidowicza 69, 8-03 Gdyia POLAND t.praczy@amw.gdyia.pl Abstract: -
More informationChapter 3 Digital Logic Structures
Copyright The McGraw-HillCompaies, Ic. Permissio required for reproductio or display. Computig Layers Chapter 3 Digital Logic Structures Problems Algorithms Laguage Istructio Set Architecture Microarchitecture
More informationSIDELOBE SUPPRESSION IN OFDM SYSTEMS
SIDELOBE SUPPRESSION IN OFDM SYSTEMS Iva Cosovic Germa Aerospace Ceter (DLR), Ist. of Commuicatios ad Navigatio Oberpfaffehofe, 82234 Wesslig, Germay iva.cosovic@dlr.de Vijayasarathi Jaardhaam Muich Uiversity
More informationNovel Modeling Techniques for RTL Power Estimation
Novel Modelig Techiques for RTL Power Estimatio Michael Eierma Walter Stechele Istitute for Itegrated Circuits Istitute for Itegrated Circuits Techical Uiversity of Muich Techical Uiversity of Muich Arcisstr.
More informationDIGITALLY TUNED SINUSOIDAL OSCILLATOR USING MULTIPLE- OUTPUT CURRENT OPERATIONAL AMPLIFIER FOR APPLICATIONS IN HIGH STABLE ACOUSTICAL GENERATORS
Molecular ad Quatum Acoustics vol. 7, (6) 95 DGTALL TUNED SNUSODAL OSCLLATOR USNG MULTPLE- OUTPUT CURRENT OPERATONAL AMPLFER FOR APPLCATONS N HGH STABLE ACOUSTCAL GENERATORS Lesław TOPÓR-KAMŃSK Faculty
More informationH2 Mathematics Pure Mathematics Section A Comprehensive Checklist of Concepts and Skills by Mr Wee Wen Shih. Visit: wenshih.wordpress.
H2 Mathematics Pure Mathematics Sectio A Comprehesive Checklist of Cocepts ad Skills by Mr Wee We Shih Visit: weshih.wordpress.com Updated: Ja 2010 Syllabus topic 1: Fuctios ad graphs 1.1 Checklist o Fuctios
More informationRoberto s Notes on Infinite Series Chapter 1: Series Section 2. Infinite series
Roberto s Notes o Ifiite Series Chapter : Series Sectio Ifiite series What you eed to ow already: What sequeces are. Basic termiology ad otatio for sequeces. What you ca lear here: What a ifiite series
More informationImplementation of Fuzzy Multiple Objective Decision Making Algorithm in a Heterogeneous Mobile Environment
Implemetatio of Fuzzy Multiple Objective Decisio Makig Algorithm i a Heterogeeous Mobile Eviromet P.M.L. ha, Y.F. Hu, R.E. Sheriff, Departmet of Electroics ad Telecommuicatios Departmet of yberetics, Iteret
More informationCompound Controller for DC Motor Servo System Based on Inner-Loop Extended State Observer
BULGARIAN ACADEMY OF SCIENCES CYBERNETICS AND INFORMATION TECHNOLOGIES Volume 6, No 5 Special Issue o Applicatio of Advaced Computig ad Simulatio i Iformatio Systems Sofia 06 Prit ISSN: 3-970; Olie ISSN:
More informationAC : USING ELLIPTIC INTEGRALS AND FUNCTIONS TO STUDY LARGE-AMPLITUDE OSCILLATIONS OF A PENDULUM
AC 007-7: USING ELLIPTIC INTEGRALS AND FUNCTIONS TO STUDY LARGE-AMPLITUDE OSCILLATIONS OF A PENDULUM Josue Njock-Libii, Idiaa Uiversity-Purdue Uiversity-Fort Waye Josué Njock Libii is Associate Professor
More informationA New Basic Unit for Cascaded Multilevel Inverters with the Capability of Reducing the Number of Switches
Joural of Power Electroics, ol, o, pp 67-677, July 67 JPE --6 http://dxdoiorg/6/jpe67 I(Prit: 98-9 / I(Olie: 9-78 A ew Basic Uit for Cascaded Multi Iverters with the Capability of Reducig the umber of
More informationLaboratory Exercise 3: Dynamic System Response Laboratory Handout AME 250: Fundamentals of Measurements and Data Analysis
Laboratory Exercise 3: Dyamic System Respose Laboratory Hadout AME 50: Fudametals of Measuremets ad Data Aalysis Prepared by: Matthew Beigto Date exercises to be performed: Deliverables: Part I 1) Usig
More informationSpread Spectrum Signal for Digital Communications
Wireless Iformatio Trasmissio System Lab. Spread Spectrum Sigal for Digital Commuicatios Istitute of Commuicatios Egieerig Natioal Su Yat-se Uiversity Spread Spectrum Commuicatios Defiitio: The trasmitted
More informationMEASUREMENT AND CONTORL OF TOTAL HARMONIC DISTORTION IN FREQUENCY RANGE 0,02-10KHZ.
ELECTRONICS 00 September, Sozopol, BLGARIA MEASREMENT AND CONTORL OF TOTAL HARMONIC DISTORTION IN FREQENCY RANGE 0,0-0KHZ. Plame Agelov Agelov Faculty for Computer Sciece, Egieerig ad Natural Studies,
More informationDesign of modulo 2 n -1 multiplier Based on Radix-8 Booth Algorithm using Residue Number System
Desig of modulo 2-1 multiplier Based o Radix-8 Booth Algorithm usig Residue Number System K.RAMAMOHAN REDDY M.Tech Studet, Dept. of ECE Vaagdevi Istitute of Techology & Sciece,Proddatur, Kadapa (Dt.),
More informationCounting on r-fibonacci Numbers
Claremot Colleges Scholarship @ Claremot All HMC Faculty Publicatios ad Research HMC Faculty Scholarship 5-1-2015 Coutig o r-fiboacci Numbers Arthur Bejami Harvey Mudd College Curtis Heberle Harvey Mudd
More informationAdaptive Resource Allocation in Multiuser OFDM Systems
Adaptive Resource Allocatio i Multiuser OFDM Systems Fial Report Multidimesioal Digital Sigal Processig Malik Meherali Saleh The Uiversity of Texas at Austi malikmsaleh@mail.utexas.edu Sprig 005 Abstract
More informationPulse-echo Ultrasonic NDE of Adhesive Bonds in Automotive Assembly
ECNDT 6 - Poster 7 Pulse-echo Ultrasoic NDE of Adhesive Bods i Automotive Assembly Roma Gr. MAEV, Sergey TITOV, Uiversity of Widsor, Widsor, Caada Abstract. Recetly, adhesive bodig techology has begu to
More informationAcquisition of GPS Software Receiver Using Split-Radix FFT
006 IEEE Coferece o Systems, Ma, ad Cyberetics October -, 006, Taipei, Taiwa Acquisitio of GPS Software Receiver Usig Split-Radix FFT W. H. Li, W. L. Mao, H. W. Tsao, F. R. Chag, ad W. H. Huag Abstract
More information}, how many different strings of length n 1 exist? }, how many different strings of length n 2 exist that contain at least one a 1
1. [5] Give sets A ad B, each of cardiality 1, how may fuctios map A i a oe-tooe fashio oto B? 2. [5] a. Give the set of r symbols { a 1, a 2,..., a r }, how may differet strigs of legth 1 exist? [5]b.
More informationAME28461 SERIES EMI FILTER HYBRID-HIGH RELIABILITY
PD-94597A AME28461 SERIES EMI FILTER HYBRID-HIGH RELIABILITY Descriptio The AME Series of EMI filters have bee desiged to provide full compliace with the iput lie reflected ripple curret requiremet specified
More informationFingerprint Classification Based on Directional Image Constructed Using Wavelet Transform Domains
7 Figerprit Classificatio Based o Directioal Image Costructed Usig Wavelet Trasform Domais Musa Mohd Mokji, Syed Abd. Rahma Syed Abu Bakar, Zuwairie Ibrahim 3 Departmet of Microelectroic ad Computer Egieerig
More informationPower Optimization for Pipeline ADC Via Systematic Automation Design
Power Optimizatio for Pipelie AD ia Systematic Automatio Desig Qiao Yag ad Xiaobo Wu Abstract--A efficiet geeral systematic automatio desig methodology is proposed to optimize the power of pipelie Aalog-to-Digital
More information1. How many possible ways are there to form five-letter words using only the letters A H? How many such words consist of five distinct letters?
COMBINATORICS EXERCISES Stepha Wager 1. How may possible ways are there to form five-letter words usig oly the letters A H? How may such words cosist of five distict letters? 2. How may differet umber
More informationJoint Power Allocation and Beamforming for Cooperative Networks
It. J. Commuicatios, etwork ad System Scieces,, 4, 447-45 doi:.436/ijcs..4753 Published Olie July (http://www.scirp.org/joural/ijcs) Joit Power Allocatio ad Beamformig for Cooperative etworks Sodes Maadi,,
More informationCross-Entropy-Based Sign-Selection Algorithms for Peak-to-Average Power Ratio Reduction of OFDM Systems
4990 IEEE TRASACTIOS O SIGAL PROCESSIG, VOL. 56, O. 10, OCTOBER 2008 Cross-Etropy-Based Sig-Selectio Algorithms for Peak-to-Average Power Ratio Reductio of OFDM Systems Luqig Wag ad Chitha Tellambura Abstract
More informationWavelet Transform. CSEP 590 Data Compression Autumn Wavelet Transformed Barbara (Enhanced) Wavelet Transformed Barbara (Actual)
Wavelet Trasform CSEP 59 Data Compressio Autum 7 Wavelet Trasform Codig PACW Wavelet Trasform A family of atios that filters the data ito low resolutio data plus detail data high pass filter low pass filter
More informationAccelerating Image Processing Algorithms with Microblaze Softcore and Digilent S3 FPGA Demonstration Board
Acceleratig Image Processig Algorithms with Microblaze Softcore ad Digilet S3 FPGA Demostratio Board Computer Electroics 1 st Semester, 2011/2012 1 Itroductio This project itroduces a example for image
More informationTowards Acceleration of Deep Convolutional Neural Networks using Stochastic Computing
Towards Acceleratio of Deep Covolutioal Neural Networks usig Stochastic Computig Ji Li, Ao Re, Zhe Li, Caiwe Dig, Bo Yua 3, Qiru Qiu ad Yazhi Wag Departmet of Electrical Egieerig, Uiversity of Souther
More informationAnalysis of SDR GNSS Using MATLAB
Iteratioal Joural of Computer Techology ad Electroics Egieerig (IJCTEE) Volume 5, Issue 3, Jue 2015 Aalysis of SDR GNSS Usig MATLAB Abstract This paper explais a software defied radio global avigatio satellite
More informationIntegrating Machine Reliability and Preventive Maintenance Planning in Manufacturing Cell Design
IEMS Vol. 7, No., pp. 4-5, September 008. Itegratig Machie Reliability ad Prevetive Maiteace Plaig i Maufacturig Cell Desig Kacha Das East Carolia Uiversity, Greeville, NC 7858, USA 5-737-905, E-mail:
More informationWAVE-BASED TRANSIENT ANALYSIS USING BLOCK NEWTON-JACOBI
WAVE-BASED TRANSIENT ANALYSIS USING BLOCK NEWTON-JACOBI Muhammad Kabir McGill Uiversity Departmet of Electrical ad Computer Egieerig Motreal, QC H3A 2A7 Email: muhammad.kabir@mail.mcgill.ca Carlos Christofferse
More informationMultisensor transducer based on a parallel fiber optic digital-to-analog converter
V Iteratioal Forum for Youg cietists "pace Egieerig" Multisesor trasducer based o a parallel fiber optic digital-to-aalog coverter Vladimir Grechishikov 1, Olga Teryaeva 1,*, ad Vyacheslav Aiev 1 1 amara
More informationThe Firing Dispersion of Bullet Test Sample Analysis
Iteratioal Joural of Materials, Mechaics ad Maufacturig, Vol., No., Ma 5 The Firig Dispersio of Bullet Test Sample Aalsis Youliag Xu, Jubi Zhag, Li Ma, ad Yoghai Sha Udisputed, this approach does reduce
More informationA 5th order video band elliptic filter topology using OTRA based Fleischer Tow Biquad with MOS-C Realization
Natural ad Egieerig Scieces 44 olume 1, No. 2, 44-52, 2016 A 5th order video bad elliptic filter topology usig OTA based Fleischer Tow Biquad with MOS-C ealiatio Ahmet Gökçe 1*, Uğur Çam 2 1 Faculty of
More informationLETTER A Novel Adaptive Channel Estimation Scheme for DS-CDMA
1274 LETTER A Novel Adaptive Chael Estimatio Scheme for DS-CDMA Che HE a), Member ad Xiao-xiag LI, Nomember SUMMARY This paper proposes a adaptive chael estimatio scheme, which uses differet movig average
More informationPERMUTATIONS AND COMBINATIONS
www.sakshieducatio.com PERMUTATIONS AND COMBINATIONS OBJECTIVE PROBLEMS. There are parcels ad 5 post-offices. I how may differet ways the registratio of parcel ca be made 5 (a) 0 (b) 5 (c) 5 (d) 5. I how
More informationSubband Coding of Speech Signals Using Decimation and Interpolation
3 th Iteratioal Coferece o AEROSPACE SCIENCES & AVIATION TECHNOLOGY, ASAT- 3, May 6 8, 9, E-Mail: asat@mtc.edu.eg Military Techical College, Kobry Elkobbah, Cairo, Egypt Tel : +() 459 43638, Fax: +() 698
More information