Design of Compact Reversible Bidirectional Shifters for Arithmetic and Logic Unit

Transcription

1 Design of Compac Reversible Bidireci Shifers for Arihmeic and Logic Uni K.Kanham M.Tech, Dep of ECE (VLSI), BVC College of Engineering, Rajahmundry A.P. Mrs T.Neelima, M.Tech(Ph.D) Associae Professor, Dep of ECE, BVC College of Engineering, Rajahmundry A.P. ABSTRACT: The developmen in he field of nanomeer echnology leads o minimize he power consumpion of logic circuis. Reversible logic design has been one of he promising echnologies gaining greaer ineres due o less dissipaion of hea and low power consumpion. In his paper we propose an approach for he design of n- bi reversible bidireci barrel shifer using compac reversible logic gaes. The proposed bidireci barrel shifer can shif a mos (n - 1) bis using logn bis selec inpu whereas he exising reversible barrel shifers can shif a mos logn bis using he same number of selec inpus. All he synhesis and simulaion are performed on Xilinx ISE 14.7 using Verilog HDL. The proposed reversible compac barrel shifer design for Arihmeic and Logical Uni(ALU). A comparaive analysis has been presened o show he significan improvemen of our proposed design wih respec o he exising approaches in erms of numbers of gaes, garbage oupus and quanum cos. I. INTRODUCTION: Conveni combinai logic circuis dissipae hea for every bi of informaion ha is los during heir operaion. Due o his fac he informaion once los canno be recovered in any way. Bu he same circui if i is consruced using he reversible logic gaes will allow he recovery of he informaion. In 1960s R. Landauer demonsraed ha even wih high echnology circuis and sysems consruced using irreversible hardware, resuls in energy dissipaion due o informaion loss [1].He showed ha he loss of one bi of informaion dissipaes KTln2 joules of energy where K is he Bolzman s consan and T is he absolue emperaure a which he operaion is performed [1]. Laer Benne, in 1973, showed ha his KTln2 joules of energy dissipaion in a circui can be avoided if i is consruced using reversible logic circuis [2]. In reversible logic, here is a one o one mapping beween inpus and oupus and for his reason no informaion is los. Reversible logic is widely used in he fields of Quanum Compuing, Nanoechnology, DNA Compuing ec. Differen archiecures of reversible barrel shifer [1], [2], [3] have been proposed in lieraure which can roae a mos logn-bi for n-bi inpu. In his paper, a novel approach of reversible barrel shifer is proposed where maximum shif amoun is (n 1) bi. The proposed design performs roaion operaion in boh direcions and i requires less number of gaes, quanum cos and garbage oupus. II. PRIOR WORK This secion presens he basic definiions regarding reversible logic. A. Reversible Gae Reversible gae is an n-inpu and n-oupu (denoed by n n) circui ha produces a unique oupu paern for each possible inpu paern [4]. In oher words, reversible gaes are circuis in which he number of oupus is equal o he number of inpus and here is a one-o-one correspondence beween he vecor of inpus and oupus. In his paper, we use some reversible gaes, such as Feynman Gae (FG) [5], Modified Fredkin Gae (MFG) [6], Peres Gae (PG) [7], Fredkin Gae (FRG) [8] and BJN Gae [9], o design our proposed circui. Page 852

2 Figure 1. (a) Block diagram of 2x2 Feynman gae and (b) Equivalen quanum represenaion Figure 4. (a) Block diagram of 3*3 Peres and (b) Equivalen quanum represenaion. Figure 2. (a) Block diagram of 3*3 Frekdin gae and (b) Equivalen quanum represenaion Figure 5. (a) BJN Gae - 3*3 gae and (b) Quanum realizaion of BJN gae B. Garbage Oupus Unwaned or unused oupu of a reversible gae (or circui) is known as garbage oupu [10]. The garbage oupus are needed only o mainain he reversibiliy. Figure 3. (a) Block diagram of Modified FRG and (b) Equivalen quanum represenaion C. Quanum Cos The quanum cos of a reversible gae (circui) is he number of elemenary quanum gaes required o realize a reversible funcion [11]. The mos used elemenary quanum gae are NOT gae, conrolled- NOT (CNOT) gae, conrolled-v gae and conrolled V + gae. Page 853

3 III. LITERATURE SURVEY Gorgin e al. [1] proposed a reversible unidireci logarihmic barrel shifer. In ha paper, he shif value is a mos logn bis for an n-bi daa inpu and he design requires large number of gaes, quanum cos and garbage oupus. Hashmi e al. [2] proposed a reversible unidireci logarihmic barrel shifer which requires less number of gaes, quanum cos and garbage oupus han [1]. Bu, he design can roae a mos logn bis for an n-bi daa inpu. Aradhiya e al. [3] proposed a reversible barrel shifer which can perform roae and shif operaions in boh direcions. Bu no generalized design is shown in his paper and he design has more quanum cos han previous designs [1], [2]. IV. PROPOSED REVERSIBLE BIDIRECTIONAL BARREL SHIFTER This secion presens he proposed archiecure of reversible barrel shifer which performs roae operaion in boh direcions. If he daa inpu is of n-bi and he maximum shif amoun is b-bi hen he barrel shifer is defined as (n, b) barrel shifer. The selec inpu is of logn-bi which represens he shif amoun. There is one conrol inpu d ir which represens he direcion of he roaion (lef or righ). When conrol inpu d ir is 1, a lef roaion is performed. Oherwise, a righ roaion is performed. According o [12], if an n- bi daa inpu is righ roaed by b-bi, i is equivalen o an (n b)-bi lef roaion. Besides, if n is a ineger power of 2, hen (n b) is he 2 s complemen of b [13]. Based on his concep, when d ir = 1, selec inpu is 2 s complemened and a righ roaion is performed based on 2 s complemened selec inpu. When di r = 0, he selec inpu is kep unchanged. A 1-bi (S 1 = 0, S 0 = 1) righ roaion is equivalen o a 3-bi (2 s complemen of 1) lef roaion. This saemen is rue for all oher values of selec inpu as long as number of bis of daa inpu is a power of wo. The daa inpus are divided ino pairs, where bis in each pair swaps for a paricular condiion. The condiions for swapping are calculaed from he selec inpu. So, he proposed bidireci barrel shifer can be divided ino 3 componens: 1) 2 s complemen generaor, 2) swap condiion generaor and 3) righ roaor. A simplified block diagram is shown in Figure 6 o realize he bidireci barrel shifer. The deail circui of he proposed reversible bidireci barrel shifer is presened in laer secions. Figure 6: Simple Block Diagram of he Proposed Barrel Shifer A. Proposed Reversible 3 3 Modified BJN Gae We propose a 3 3 reversible Modified BJN gae (MBJN) o minimize he quanum cos of he proposed reversible 2 s complemen generaor. This gae is a modified version of exising reversible BJN gae [9]. The proposed gae maps hree inpus (A, B, C) o hree oupus (A, A B, (A+B) C) and mainains a one-oone relaionship beween hem. Figure 7 (a) and 2 (b) represen he block diagram and quanum realizaion of proposed reversible MBJN gae. The proposed MBJN gae requires quanum cos of 4. Figure 7: (a) Block Diagram and (b) Quanum Realizaion of Proposed Reversible MBJN Gae Page 854

4 B. Proposed Reversible 2 s Complemen Generaor According o [13], he 2 s complemen of a binary number can be calculaed in wo seps: 1) find 1 s complemen by complemening each bi and 2) addiion of 1 o he leassignifican-bi (lsb) posiion. In his paper, 2 s complemen of he selec inpu is generaed wihou using any adder circuiry. Algorihm 1 is presened o generae 2 s complemen of lognbi selec inpu of an n-bi barrel shifer. Figure 8: (a) 2-Bi and (b) 3-Bi Reversible 2 s Complemen Generaor Le, he 2 s complemen of selec inpu Si be C i, where 0 i logn 1. According o Algorihm 1, he lsb (S0) of he selec inpu is equivalen o i s 2 s complemen. If index i is one, he 2 s complemen of Si is he XOR of he lsb and he bi iself. To generae he bis a index i 2, he corresponding bi is XORed wih he OR of all bis a lower posiions. For example, he 2 s complemen of bi S 2 is S 2 (S 1 + S 0 ). If conrol inpu dir is zero, selec inpu Si is reurned. Oherwise, 2 s complemen of selec inpu is reurned, where, 0 i logn 1. A 2-bi and 3-bi 2 s complemen generaor as shown in Figure 8 (a) and 3 (b). Proposed 2 and 3-bi reversible 2 s complemen generaor needs oal 3 and 5 gaes wih quanum cos of 6 and 14, respecively. Lemma 1: Le GC be he number of gaes, QC be he quanum cos and GO be he number of garbage oupus of an logn-bi reversible 2 s complemen generaor of an n-bi barrel shifer. Then, GC = 2logn 1, QC = 8logn 10 and GO = logn. C. Proposed Reversible Swap Condiion Generaor This uni generaes swap condiions o swap bis in a pair of daa inpus in n(> 4)-bi righ roaor uni. The oupus of 2 s complemen generaor are fed o swap condiion generaor as inpus. An n-bi daa inpu can be divided ino n/2 number of pairs. Since each pair needs a paricular swap condiion, we need oal n/2 number of condiions. A mehodology o implemen a swap condiion generaor is explained wih he following example: Inpu: Oupus of 2 s complemen generaor C logn 1 o C 0. Oupu: Swap condiions SC n/2 1 o SC 0. Sep 1: Swap condiion for pair0 is he msb of he selec inpu and swap condiion for pair n 4 is 2nd msb Page 855

5 of he selec inpu. For example, a 16-bi daa inpu needs 8 swap condiions where, SC 0 = C 3, SC 4 = C 2. Sep 2: For Swap condiions ha are greaer han zero and less han n/4, perform C logn 2 AND oupus of (logn 1)- bi swap condiion generaor ha are greaer han zero. For example, an 8-bi daa inpu has 3-bi selec inpu and swap condiions are, SC 0 = C 2, SC 1 = (C 1 AND C 0 ), SC 2 = C 1, SC 3 = (C 1 OR C 0 ). Similarly, a 16-bi daa inpu has 4-bi selec inpu and is swap condiion is less han four, which are SC1= C 2 AND (C 1 AND C 0 ), SC 2 = C 2 AND C 1, and so on. Sep 3: For Swap condiions ha are greaer han n/4, perform C logn 2 OR oupus of (logn 1)-bi swap condiion generaor ha are greaer han zero. A 16-bi daa inpu has 4-bi selec inpu and is swap condiion is greaer han four, which are SC 5 = C 2 OR (C 1 AND C 0 ), SC 6 = (C 2 OR C 1 ), and so on. A 3-bi and a 4-bi reversible swap condiion generaors are shown in Figures 9 and 10. oupus of an logn-bi reversible swap condiion generaor of an n-bi reversible barrel shifer. Then, GC = n 2logn, QC = 9( n/2 logn) and GO = n/2 logn. D. Proposed Reversible Righ Roaor An n-bi (n > 4) righ roaor akes an n-bi daa inpu, oupus of 2 s complemen generaor and oupus of swap condiion generaor o roae a mos b(= n 1) bis in righ direcion. In his secion, firs a (4, 3) reversible righ roaor is presened and hen a generalized approach is developed. 1) Proposed (4, 3) Reversible Righ Roaor: A (4, 3) reversible righ roaor akes 4-bi daa inpu, 2-bi selec inpu from 2 s complemen generaor and roaes a mos hree bis as shown in Figure 11. The swap condiion generaor is no needed for a (4, 3) reversible righ roaor. The proposed circui needs 5 gaes wih 21 quanum cos and i generaes 2 garbage oupus. Proposed (4, 3) reversible righ roaor is used o realize an nbi reversible righ roaor. Figure 9: 3-Bi Reversible Swap Condiion Generaor Figure 11: A (4,3) Reversible Righ Roaor Figure 10: 4-Bi Reversible Swap Condiion Generaor Lemma 2: Le GC be he number of gaes, QC be he quanum cos and GO be he number of garbage 2) Proposed Generalized Reversible Righ Roaor: A mehodology o implemen a righ roaor is explained wih he following example: Inpu: Daa inpus a n 1 o a 0, oupus of 2 s complemen generaor C logn 1 o C 0, oupus of swap condiion generaor SC n/2 1 o SC 0. Oupu: Righ Roaed Oupus R n 1 o R 0. Sep 1: Pariion n-bi daa inpu ino wo groups and ake one bi from he 1s pariion and one bi from he 2nd pariion o form a pair. Page 856

6 Sep 2: Call he algorihm swap condiion presened in Secion IV-C. Bis in a pair are swapped if XOR of corresponding swap condiion and msb of he selec inpu is 1. Sep 3: Take he 1s bi of all pairs o form pariion 1 and 2nd bi of all pairs o form pariion 2. The bis in 1s pariion and selec inpu excep he msb are fed o an n 2 -bi righ roaor. Similarly, he bis in 2nd pariion and selec inpu excep he msb are fed o an n 2 -bi righ roaor. An n 2 -bi righ roaor is called recursively unil n becomes 4. When, n becomes 4, we need a 4-bi righ roaor which is shown in Figure 11. The 1s roaor generaes oupus Rn 1 o R n/2 and he 2nd roaor produces oupus R n/2 1 o R 0. Lemma 3: Le GC be he number of gaes, QC be he quanum cos and GO be he number of garbage oupus of an n-bi reversible righ roaor uni. Then, GC = ( 3n /4 7)logn + 5n/2 + 3, QC = (3n 29)logn + 19n/ and GO = ( n/2 3)logn + n/ V. 8-BIT PROPOSED REVERSIBLE BIDIRECTIONAL BARREL SHIFTER In his secion, he whole archiecure of he proposed reversible bidireci barrel shifer is presened. The hree reversible componens discussed in previous secions are combined o implemen he proposed reversible bidireci barrel shifer. The archiecure of proposed reversible (8, 7) bidireci barrel shifer is depiced in Figure 12. So, he reversible circuis presened in Secion IV-B, IV-C and IV-D can be combined wih addii FG gaes o realize a generalized reversible bidireci barrel shifer. The propery of he proposed n-bi reversible bidireci barrel shifer is presened in Lemma 4 o calculae he cos parameers such as gae coun, quanum cos and garbage oupus. Lemma 4: Le GC be he number of gaes, QC be he quanum cos and GO be he number of garbage oupus of an n- bi reversible bidireci barrel shifer. Then, GC = ( 3n/ 4 7)logn + 7n/2 + 2, QC = (3n 30)logn + 14n + 7 and GO = ( n/2 3)logn + n + 2. VI. COMPARATIVE STUDY This secion analyzes he proposed design of reversible bidireci barrel shifer wih exising designs in erms of gae coun, quanum cos and garbage oupus. We compare he proposed reversible bidireci 4-bi and 8-bi barrel shifers. TABLE I: Comparison of Differen 4-Bi Reversible Barrel Shifers Properies Propo sed ng [1] ng [2] ng [3] Ga e Cou n Garb age Oup us Quan um Cos Bidirecio nal Unidireci Unidireci Bidirecio nal Figure 12: Block Diagram of (8, 7) Reversible Bidireci Barrel Shifer Page 857

7 TABLE II: Comparison of Differen 8-Bi Reversible Barrel Shifers Properies Propo sed ng [1] ng [2] Ga e Cou n Garb age Oup us Quan um Cos Bidirecio nal Unidireci Unidireci TABLE III: Comparison of Differen 16-Bi Reversible Barrel Shifers Properies Propo sed ng [1] Ga e Cou n Garb age Oup us Quan um Cos Bidirecio nal Unidireci From Table I and II, we find ha our proposed 4-bi, 8- bi and 16 bi reversible bidireci barrel shifers require less number of gaes, less quanum cos and produces less garbage oupus han exising designs [1], [2] and [3]. For example, he proposed 4-bi reversible barrel shifer is improved by 66.67%, 20% and 27.27% han exising designs [1], [2] and [3] in erms of gae coun. Similarly, he proposed 8-bi reversible barrel shifer is improved by 74.10% and 19.44% han exising designs [1] and [2] in erms of gae coun. Moreover, he proposed 8-bi reversible barrel shifer can shif up o 8 1 = 7 bis whereas, he exising designs [1] and [2] can shif up o log8 = 3 bis only. VII. SIMULATION RESULTS: All he synhesis and simulaion resuls of he Proposed Reversible 16bi Bidireci Barrel Shifers are performed using Verilog HDL. The synhesis and simulaion are performed on Xilinx ISE The corresponding simulaion resuls of Proposed Reversible 16bi Bidireci Barrel Shifers are shown below. Figure 13: RTL schemaic of Top-level of Proposed Reversible 16bi Bidireci Barrel Shifer Figure 14: RTL schemaic of Inernal block of Proposed Reversible 16bi Bidireci Barrel Shifer Figure 15: Technology schemaic of Inernal block of Proposed Reversible 16bi Bidireci Barrel Shifer Page 858

8 Figure 16: Synhesis summary repor of Proposed Reversible 16bi Bidireci Barrel Shifer logic which can be used in arihmeic circuis for signed number. Two algorihms have been presened o realize a cos efficien reversible bidireci barrel shifer. A comparaive sudy beween exising and proposed works has been presened o show he efficiency of he proposed work. The proposed 8-bi reversible barrel shifer is improved by more han 50% in erms GC,QC and GO han exising designs [1]. Our proposed reversible barrel shifer can be used in reversible arihmeic logic uni which is a hear of a reversible processor. Besides, i can be used in oher reversible arihmeic circuis for shifing operaion [1], [2]. REFERENCES [1] S. Gorgin and A. Kaivani, Reversible barrel shifers, in Compuer Sysems and Applicaions, AICCSA 07. IEEE/ACS Inernai Conference on, May 2007, pp Figure 17: Tes Bench for Proposed Reversible 16bi Bidireci Barrel Shifer Figure 18: simulaed oupus for Proposed Reversible 16bi Bidireci Barrel Shifer VIII. CONCLUSIONS: This paper presened he design mehodology of an efficien and generalized reversible barrel shifer. In he way of presening he proposed design, a 2 s complemen generaor is implemened using reversible [2] I. Hashmi and H. M. H. Babu, An efficien design of a reversible barrel shifer, in VLSI Design, VLSID rd Inernai Conference on. IEEE, 2010, pp [3] H. V. R. Aradhya, J. Lakshmesha, and K. N. Muralidhara, Design opimizaion of reversible logic universal barrel shifer for low power applicaions, Inernai Journal of Compuer Applicaions, vol. 40, no. 15, pp , February [4] P. Kernopf, A new heurisic algorihm for reversible logic synhesis, in Proceedings of he 41s annual Design Auomaion Conference. ACM, 2004, pp [5] R. P. Feynman, Quanum mechanical compuers1, Foundaions of Physics, vol. 16, no. 6, p. 986, [6] M. S. Al Mamun, I. Mandal, and M. Hasanuzzaman, Design of universal shif regiser using reversible logic, Inernai Journal of Page 859

9 Engineering and Technology, vol. 2, no. 9, pp , Sepember [7] A. Peres, Reversible logic and quanum compuers, Physical review A, vol. 32, no. 6, pp , [8] E. Fredkin and T. Toffoli, Conservaive logic. Springer, [9] A. N. Nagamani, H. V. Jayashree, and H. R. Bhagyalakshmi, Novel low power comparaor design using reversible logic gaes, Indian Journal of Compuer Science and Engineering, vol. 2, no. 4, pp , AugusSepember [10] D. Maslov and G. W. Dueck, Garbage in reversible design of muliple oupu funcions, in 6h Inernai Symposium on Represenaions and Mehodology of Fuure Compuing Technologies, 2003, pp [11] M. A. Nielsen and I. L. Chuang, Quanum compuaion and quanum informaion. Cambridge universiy press, [12] T. Thomson and H. Tam, Barrel shifer, Jul , us Paen 5,652,718. [13] R. J. Tocci, Digial Sysems: principles and applicaions. Pearson Educaion India, Page 860