EVOLUTION OF STRUCTURE OF SOME BINARY GROUP-BASED N-BIT COMPARATOR

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Reversible logic has attracted substantial interest due to its low power consumption which is the main concern of low power VLSI systems. In this paper, a novel 4x4 reversible gate called inventive gate has been introduced and using this gate 1-bit, 2-bit, 8-bit, 32-bit and n-bit group-based reversible comparator have been constructed with low value of reversible parameters. The MOS transistor realizations of 1-bit, 2- bit, and 8-bit of reversible comparator are also presented and finding power, delay and power delay product (PDP) with appropriate aspect ratio W/L. Novel inventive gate has the ability to use as an n-to-2n decoder. Different novel reversible circuit design style is compared with the existing ones. The relative results shows that the novel reversible gate wide utility, group-based reversible comparator outperforms the present style in terms of number of gates, garbage outputs and constant input.

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International Journal of VLSI design Communication Systems VLSICS Vol.5 No.5 October 2014 DOI : 10.5121/vlsic.2014.5502 9 EVOLUTION OF STRUCTURE OF SOME BINARY GROUP-BASED N-BIT COMPARATOR N-TO-2 N DECODER BY REVERSIBLE TECHNIQUE Neeraj Kumar Misra 1 Subodh Wairya 2 and Vinod Kumar Singh 3 Department of Electronics Engineering Institute of Engineering and Technology Lucknow India ABSTRACT Reversible logic has attracted substantial interest due to its low power consumption which is the main concern of low power VLSI systems. In this paper a novel 4x4 reversible gate called inventive gate has been introduced and using this gate 1-bit 2-bit 8-bit 32-bit and n-bit group-based reversible comparator have been constructed with low value of reversible parameters. The MOS transistor realizations of 1-bit 2- bit and 8-bit of reversible comparator are also presented and finding power delay and power delay product PDP with appropriate aspect ratio W/L. Novel inventive gate has the ability to use as an n-to-2n decoder. Different novel reversible circuit design style is compared with the existing ones. The relative results shows that the novel reversible gate wide utility group-based reversible comparator outperforms the present style in terms of number of gates garbage outputs and constant input. KEYWORDS Reversible Logic Inventive Gate Garbage Output Constant input Full subtractor n-bit reversible comparator Reversible decoder etc. 1. INTRODUCTION In low power VLSI systems planning of power is one of important aspects. According to Landauer 1 in 1960 demonstrate that single bit of information loss generate at least KT ln2 J/K of energy where K is the Boltzmann constant 1.38x10 -23 J/K and T is the absolute temperature. Reversible circuits are totally different from irreversible circuits. In reversible logic no bits is loss the circuit that doesnt loss information is reversible. C.H Bennet 2 in 1973 proves that KT ln2 joule of energy wouldnt be dissipated if the reversible circuit consist of reversible gates only. Thus reversible logic operations do not loss information and dissipate less heat also as power. Thus reversible logic is probably going to be in demand in high speed power aware circuits. A reversible circuit planning has following important attributes Garbage output number of reversible gates constant input all should be minimum for efficient reversible circuits. Comparator has wide applications in Analog and digital circuits Analog to digital A/D converters Level shifter and communication system etc. It compares the 2-number of several

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International Journal of VLSI design Communication Systems VLSICS Vol.5 No.5 October 2014 10 bits. In this paper introduce group-based n-bit reversible comparator 6911 and n-to-2 n reversible decoder with low value of reversible parameters with the help of lemmas. This paper is organised with the following sections: Section 2 and 3 discuss basic definition of reversible logic and parameter optimization taken Section 4 discuss the past work Section 5 discuss the utility and design issue of novel 4x4 inventive gate Section 6 Planning of low value style reversible comparator subsection of 6.1 introduce novel 1-bit comparator cell subsection 6.2 and 6.3 is novel match larger and smaller comparator cell design Subsection 6.4 6.5 6.6. 6.7 for 2-bit 8-bit 32-bit and n- bit group-based reversible comparator design respectively Section 7 Implement all comparator cell in MOS transistor with minimum MOS transistor count. Section 8 categories as simulation result of comparator. Finally the paper is concluded and future work with Section 9. 2. BASIC DEFINITIONS OF REVERSIBLE LOGIC In this section we introduce the essential definitions of reversible logic which are relevant with this research work. Definition 2.1 A reversible gate is a Z - input and Z - output that generate a unique output pattern for each possible input pattern. Definition 2.2 In Reversible logic output and input is equal in number. Unwanted output is called garbage output it should be minimum as possible and fan-out is not allowed. 3. PARAMETER OPTIMIZED FOR DESIGNING EFFICIENT REVERSIBLE CIRCUITS The main challenge of designing efficient reversible circuits is to optimize the different reversible parameters which result the circuit design is costly. The most necessary parameters which have dominant in efficient reversible logic circuits are: 3.1 Garbage output Unutilized or unwanted output of reversible circuit is called garbage output. It should be kept minimum as possible. 3.2 Constant Input Constant bits are additional inputs that are not part of the original specification. These bits are added in hopes to reduce the circuit complexity or realize a reversible function. They come in the form of a constant logic 1 or 0. It is ideal to keep in minimal. 3.3 Few Reversible gates utilized In this subsection we present few reversible gates that are used to design for planning different types of reversible circuit. First TR 3×3 utilize input A B C and carry output PA QA⊗B RAB’⊗C Second BME gate4X4 utilize input A B C D and carry output PA

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International Journal of VLSI design Communication Systems VLSICS Vol.5 No.5 October 2014 11 QAB⊗C RAD⊗C and SA’B⊗C⊗D Third Feynman gate FG 2x2 utilize input A B and carry output PA QA⊗B Fourth Peres gate PG 3x3 utilize input A B C and carry output PA QA⊗B RAB⊗C 3.4 Flexibility Flexibility refers to the universality of reversible logic gate in realizing more logical function. 4. PAST WORK In 2010 Himanshu thapliyal et.al 17 design a reversible 8-bit and 64-bit tree-based comparator using TR Gate that has the latency of Olog2n.But this approach is not suitable for low value of reversible parameter and not extended for n-bit reversible comparator. Furthermore another comparator design by Rangaraju H Ga 7 8 in 2011 has shows that design has input circuit as first stage and 1-Bit comparator cell as second stage and so on. This idea is extend for n-bit reversible comparator design but it is not sufficient to optimizing the reversible parameter. In 2011 Nagamani et.al. 21 Design a reversible 1-bit reversible comparator with low value of reversible parameter but this idea is not extended for n-bit comparator. In 2013 Ri-gui Zhou et.al. 5 design a novel 4-bit reversible comparator. It is mentioned in paper further possibilities of reducing the number of reversible gates constant input and garbage output in the area of reversible comparator design. They proposed new gate and using this gate form various gate AND OR XNOR NOT FA FS but not form gate NAND NOR. For increasing order of comparator gate increase in higher order and complexity of design increases and also garbage outputs means performance of comparator degrade. In 2013 Hafiz Md. Hasan babu et.al. 4 design compact n-bit reversible comparator. Its design is efficient because it reduce complexity of design. Approach is sufficient and proposed various theorem and lemma for calculating n-bit reversible parameter number of gate total delay power. They proposed two new gate BJS and HLN. These gate form OR AND XOR and NOT Operation but not form FA FS NAND and NOR Operation. For showing expertise of reversible gate we work on this and proposed Universal gate called Inventive Gate. It’s performing all logical operation NAND NOR AND OR HA HS FA and FS and also form efficient group- based n-bit reversible comparator and n-to-2 n bit decoder with low value of reversible parameters. 5. UTILITY AND DESIGN ISSUES OF FRESHLY PROJECTED 4X4 INVENTIVE GATE In this section a new 4 x 4 reversible gates called Inventive gate is proposed. The block representation of inventive gate is shown in Figure 1.The corresponding truth table shown in Table 1. And subsequent four logical configuration is presented Pa⊗b⊗c Qa⊗b⊗dc+ba⊗d Rcb+da+bc and Sb’d’a+c+db+a’c’ of inventive gate. It is shown from the truth table that the attainable output pattern can be uniquely determined.

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International Journal of VLSI design Communication Systems VLSICS Vol.5 No.5 October 2014 12 Figure 1. Block representation of Reversible 4 × 4 Inventive Gate Table 1 Reversibility of the novel Inventive gate 5.1 Utility-1 of Inventive gate The proposed Inventive gate can implement all Boolean expression and it is a universal gate. In this paper Inventive gate is used to design the n-to-2 n decoder Shown in section 5.2 and 1-bit comparator Shown in section 6.1. The classical operations realized using Inventive gate is shown in Fig a b c d e f g and h. Fig a. AND NAND gates Implementation Fig b. XOR AND NOT OR gates Implementation INPUT OUTPUT d c b a P Q R S 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 1 0 1 0 1 0 0 0 1 1 0 1 0 0 0 1 0 0 1 0 1 1 0 1 0 1 0 1 0 1 0 1 1 0 0 1 1 0 0 1 1 1 1 1 1 0 1 0 0 0 0 0 1 1 1 0 0 1 1 0 0 0 1 0 1 0 1 1 0 1 1 0 1 1 0 0 0 1 1 1 0 0 1 1 0 0 1 1 0 1 0 0 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1

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International Journal of VLSI design Communication Systems VLSICS Vol.5 No.5 October 2014 13 Fig c. NOR gate Implementation Fig d. XNOR AND gates Implementation Fig e. Half adder Implementation Fig f. Half substractor Implementation Fig g. Full adder Implementation Fig h. Full substractor Implementation 5.2. Utility-2 of Reversible inventive gate as Reversible n-to-2 n decoder In this section we show the utility-2 of Inventive gate. It performs the operation of Reversible 2- to-2 2 decoder it consists of two approaches named approach - 1 and approach - 2. Approach- 1 of 2-to-2 2 decoder generate 2 garbage output and number of gate count is 5. Whereas the Approach - 2 generate 2 garbage output but reduces number of gate count is 4 as shown in Figure 2 b. And also implement of 3-to-2 3 decoder Approach 2 generate 3 garbage output and number of gate count 7 as shown in Figure 4 .Decoder 31114 are widely used in applications like information multiplexing 7 segment show and memory addressing. 5.2.1 Reversible 2-to-2 2 decoder and 3-to-2 3 decoder Planning of Reversible 2-to-2 2 decoder is shown in Figure 2b. It consists of 1 inventive gate+ 2NOT+ 1 FG+ 1TG types of gates. It has two input marked a b apply to inventive gate and Feynman gate FG respectively obtained output is passed to TG and gives output is ab other output of decoder is a b a b and a b. Completed cell of 2-to-2 2 decoder are named as I_F_T decoder cell. These cell are utilize for designing 3-to-2 3 decoder as shown in Figure 4. Lemma 5.2.1.1 An n-to-2 n reversible decoder Approach 1 may be accomplished by a minimum of 2 n + 2 reversible gates where n is that the range of bits and n ≥ 2 Proof. We ensure the above statement by mathematical induction.

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International Journal of VLSI design Communication Systems VLSICS Vol.5 No.5 October 2014 14 For 2-to-2 2 decoder n 2 decoder Approach- 1 is made exploitation 1 inventive gate+ 2NOT+ 2 FG+ 1TG types of gates needs a minimum of 6 2 n + 2 reversible gate. Therefore the statement assert for the base value of n2. Accept the statement for n y thus a y-to-2 y decoder may be realized by a minimum of 2 y + 2 reversible gates. For y+1-to-2 y+1 decoder is made exploitation y- to -2 y decoder and 2 y FRG Gate. So the Total number of gates needed to construct a y+1 - to- 2 y+1 decoder is a minimum of 2 y + 2+2 y 2 y+1 +2 So the statement hold for n y+1 Lemma 5.2.1.2 An n-to-2 n reversible decoder Approach - 2 may be accomplished by a minimum of 2 n +1 reversible gates where n is that the range of bits and n≥2 Proof. We ensure the above statement by mathematical induction. For 2-to-2 2 decoder n 2 decoder Approach -2 is made exploitation 1 inventive gate+ 2NOT+1 FG+1TG type of gates needs a minimum of 5 2 n +1 reversible gate. Therefore the statement assert for the base value of n2. Accept the statement for n y thus a y-to-2 y decoder may be realized by a minimum of 2 y +1 reversible gate. For y+1-to-2 y+1 decoder is made exploitation y-to-2 y decoder and 2 y FRG Gate. So the total range of gates needed to construct a y+1-to-2 y+1 decoder is a minimum of. 2 y +1+2 y 2 y+1 +1 So the statement hold for n y+1 and more powerful than approach 1 because it less number of gate count. Lemma 5.2.1.3 An n-to-2 n reversible decoder Approach -2 may be accomplished by a minimum of n garbage output where n is that the range of bits and n ≥ 2 Proof. We ensure the above statement by mathematical induction. For 2-to-2 2 decoder has garbage output 2 n for the base value of n 2. For higher order decoder 3-to-2 3 garbage output 3 n for n3 Accept the statement for n k thus a k: 2 k decoder may be realized by a minimum of k garbage output.

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International Journal of VLSI design Communication Systems VLSICS Vol.5 No.5 October 2014 15 a. Approach- 1 b. Approach – 2 Figure 2. Two approaches of the Novel 2- to- 2 2 decoder Figure 3. Approach- 2 of proposed reversible 2-to-2 2 decoder Cell

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International Journal of VLSI design Communication Systems VLSICS Vol.5 No.5 October 2014 16 c. Approach- 1 d. Approach- 2 Figure 4. Two Approaches of the proposed 3 -to- 2 3 decoder Figure 5. Approach - 2 of proposed reversible n -to- 2 n decoder 6. NOVEL DESIGN OF GROUP-BASED REVERSIBLE N-BIT BINARY COMPARATOR Following section we have to project a low value of group-based reversible n-bit comparator. 6.1 Novel 1-bit reversible comparator cell design Novel 1-bit group-based reversible comparator structure uses 3 gates of 2 types 1 inventive+ 2 NOT .It is true that ab’ for ab a’b for ab and a⊙b for ab. The proposed architecture has

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International Journal of VLSI design Communication Systems VLSICS Vol.5 No.5 October 2014 17 constant input of 2 Garbage output of 1 and number of gate count 3. The structure of 1-bit comparator modelled as I_N Comparator cell. As shown in Figure 6 a 6.2 Novel 1- bit Match and larger reversible comparator cell design Novel 1-bit match and larger comparator structure use 4 Gate of 4 types 1 TR+ 1 NOT+1 BME+1 FG .First reversible TR gate use n- 1 th bits of two logic input a and b it produce two significant output a⊙b and ab’ first output is not utilize is called garbage output. Two more n th bit input P n and Q n of previous comparator result is applied to reversible BME Gate it produce two significant output Q n-1 Q n a⊙b and Q n ab’ only Q n-1 output save and other output Q n a b’ is applied to another reversible Feynman gate FG and another n th bit input P n input is selecting give one significance output P n-1 Q n a b’ ⨂ P n these two output P n-1 and Q n-1 is utilizing further for designing lesser logic comparator design. The proposed architecture has constant input of 2 garbage output of 4 and number of gate count 4 1+1+1+1. The structure of Larger and Match design modelled as TR_BME_FG Comparator cell. As shown in Figure 6 b 6.3 Novel 1-bit smaller reversible comparator cell design Novel single bit smaller reversible comparator structure use 4 gate of 2 type 3 FG + 1 NOT.These structure utilize two input P and Q and give two significant output P and P⨂Q second output P ⨂ Q is passed to NOT gate gives P ⊙ Q other output is P and Q for match operation use P Larger operation Q and lesser operation P⊙Q. The novel design has constant input of 1 Garbage output of 0 and Number of gate count 3 1+1+1. The structure of lesser cell modelled as F_F Comparator cell. As shown in Figure 6 c 6.4 Novel Efficient 2-bit reversible comparator design Design methodology of 2-bit group- based comparator cell used three cell pervious section named I_N Comparator cell TR_BME_FG Comparator cell and F_F Comparator cell these cell are connect and gives significant output PQ and R for Match Smaller and Larger logic. The novel design is shown in Figure. 6 d a

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International Journal of VLSI design Communication Systems VLSICS Vol.5 No.5 October 2014 18 b c d Figure 6. Reversible group-based 2-bit comparator design a. Reversible 1-bit Comparator. b. Match and Larger Cell design using TR_BME_FG Cell. c. Smaller Comparator Cell design using F_F Cell. d. Reversible 2-bit Comparator. 6.5 Novel architecture of Reversible 8-bit group-based Comparator Following the extremely comparable analogous approach kept in mind then we are design structure of 8-bit group-based Comparator module. The main projected structure for the 8-bit Comparator is anticipated in Figure 7. The proposed architecture has constant input of 17

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International Journal of VLSI design Communication Systems VLSICS Vol.5 No.5 October 2014 19 1×2+2×7+1 Garbage output of 29 1+ 4×7+ 1×0 and Number of gate count 34 1×3+4×7+1×3 1 0 7 b 2 Q 2 Q 2 Q 7 a 8 a 8 b 6 a 6 b 5 a 5 b 4 a 4 b 3 a 3 b 2 a 2 b 1 a 1 b 0 E P G Q L Q P ο 1 P 1 Q 8 P 8 Q 7 P 7 Q 6 P 6 Q 5 P 5 Q 4 P 4 Q 3 P 3 Q 2 P 1 P 1 Q 2 Q Figure 7. Novel architecture of Reversible 8-bit Comparator 6.6 Novel architecture of Reversible 32-bit Group-based Comparator structure. For the implementation methodology of 32-bit group-based comparator design use 1 I_N Comparator Cell+ 31 TR_BME_FG Comparator cell+1 F_F Comparator cell .The main projected structure for the 32-bit binary group-based comparator cell is anticipated in Figure 8.

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International Journal of VLSI design Communication Systems VLSICS Vol.5 No.5 October 2014 20 The proposed architecture has constant input of 65 1×2+ 2×31+ 1×1 Garbage output of 125 1×1+ 4×31+ 1×0 and Number of gate count 33 1+ 31+ 1 1 0 0 E P G Q L Q P ο 1 P 1 Q Figure 8. Novel architecture of group-based reversible 32- bit Comparator 6.7 Novel architecture of Reversible n- bit group- based Comparator structure

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International Journal of VLSI design Communication Systems VLSICS Vol.5 No.5 October 2014 21 Following the extremely comparable analogous approach we are proposing n- bit group-based comparator structure. First idea is replenishment to the main projected structure for the n-bit group-based comparator structure is anticipated in Figure 9. For designing 32-bit tree comparator cell consist of n th single bit to I_N comparator cell and n-1 n-2 n-3………..n-31 th single bit apply to TR_BME_FG Comparator cell where n is 32 for 32-bit comparator. This concept is apply for n-bit group-based comparator it consist of n th single bit to I_N comparator cell and n- 1 n-2 n-3………..n-31………….n-y th single bit apply to TR_BME_FG comparator cell where yn-1 Figure 9. Novel n- bit group- based reversible Comparator The steps to style a n-bit group-based comparator are describe in Algorithm 1. Algorithm1. Group- based n-bit Reversible Comparator 1 Pick up I_N Comparator cell and acquire input a n and b n 2 Pick up TR_BME_FG Comparator cell and takes n- 1 th bits of 2-binary variety a n-1 and b n-1 and 2 additional input Pn and Qn from previous comparison result. 3 TR_BME_FG Comparator cell 2-output Pn-1 and Qn-1 that indicates whether the given binary number are equal to one another or larger. 4 Pick up F_F Comparator cell and takes input P Q it offers output P For Equal LLess P⊙Q and G For Greater. Lemma 6.7.1 An n-bit group-based reversible comparator may be accomplished by a 6+4 n-1 number of gate 1+4 n-1 garbage output where n is the range of bits and n ≥ 2 Proof: We ensure the above statement by mathematical induction. An n-bit reversible comparator has number of gate 6+ 4 n-1. For realisation of 2-bit and 8-bit reversible comparator setting n2 8 alternatively gives 10 and 34 number of gate.

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International Journal of VLSI design Communication Systems VLSICS Vol.5 No.5 October 2014 22 An n-bit reversible comparator has garbage output 1+ 4 n-1 .For realisation of 2-bit and 8-bit reversible comparator setting n2 8 alternatively give 5 and 29 number of garbage output. Lemma 6.7.2 An n-bit group-based reversible comparator requires 85.816n – 78.989 µW power where n is the range of bits and n ≥ 2 Proof: Novel n-bit group-based comparator uses I_N Comparator cell n– 1 TR_BME_FG Comparator cell and one F_F Comparator cell. Total power relished by following specified equation Total Power P P I_N Cell + n-1 P TRE_BME_FG Cell + P F_F Cell All Comparator cell implement in MOS transistor and finding power using T-Spice tool for 90nm technology node. We have computed the power of I_N comparator cell TRE_BME_FG Comparator cell and F_F Comparator cell that are 3.358 85.816 and 3.470 µW respectively. Now the total power P of an n-bit group-based comparator as below P 3.35 + n – 1 85.81+ 3.4702 µW 3.35 +85.81n – 85.81 + 3.4702 µW 85.81n – 78.98 µW Lemma 6.7.3 An n-bit group-based reversible comparator may be accomplished by a Timing delay T of 115.010 n – 100.854 ns where n is the range of bits and n≥2 Proof: Novel n-bit group-based Comparator uses I_N Comparator cell n– 1 TR_BME_FG Comparator cell and one F_F Comparator cell .Total delay T relished by following specified equation Total delay T T I_N Cell + n – 1 T TRE_BME_FG Cell + T F_F Cell All Comparator cell implement in MOS transistor and finding delay using T-Spice tool for 90nm technology node. We have computed the power of I_N comparator cell TRE_BME_FG Comparator cell and F_F Comparator cell that are 12.51 115.010 and 1.608 ns respectively. Now the delay of an n-bit group-based comparator as below T 12.51+ n –1 115.010 + 1.608 ns 12.51+ 115.010 n – 115.010 + 1.608 ns 115.010 n – 100.854 ns

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International Journal of VLSI design Communication Systems VLSICS Vol.5 No.5 October 2014 23 7. MOS TRANSISTOR IMPLEMENTATION OF DIFFERENT COMPARATOR CELL In this section implement different comparator cell in MOS transistor with minimum MOS transistor count. MOS transistor implementations of 2-bit comparator uses 14 MOS transistors Algorithm- 2 Reversible group-based n-bit comparator Design a n-bit reversible binary comparator when n ≥ 2 with minimum number of gates and garbage output. Begin Step 1. Pick up I_N comparator cell and pick input X n and output Y n for two n-bit number X n 1 a n //n th input of a n Xn2 b n //n th input of b n X n 3 0 X n 4 1 If X n 1 X n 2 then Y n 2 R yn 1 Else if X n 1 X n 2 then Y n 4 Q yn 1 Else Y n 1 P yn 1 End if Step 2. For TR_BME_FG and F_F Comparator cell Level of input and output are considered to be Y n and Y n-1 respectively Loop For j n - 1 to 1 Pick up TR_BME_FG Comparator cell W J If j n-1 then W J 1 X n 4 Q Yn W J 2 X n 1 P Yn W J 3 b n-1 W J 4 a n-1 Else W J 1 W J-1 2 Q Yn-1 W J 2 W J-1 1 P Yn-1 W J 3 a j //n-1 th input of a n W J 4 b j //n-1 th input of b n End if End loop Step 3. Pick up F_F Comparator cell and pick input V and output Z V1 W1 V2 W2 V3 0 Z1 W1 Z2 W1⊗ W2⊗ 1 Z3 W2 End

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International Journal of VLSI design Communication Systems VLSICS Vol.5 No.5 October 2014 24 TR_BME_FG Comparator cell required 18 MOS transistor and for F_F comparator cell require 4 MOS transistor. These cells are connected for required 2-bit 8-bit and 64-bit reversible comparator operation and analyzed in terms of power consumption delay and power delay product PDP. Figure 10. MOS transistor implementation of Figure 11. MOS transistor implementation of 1- bit Comparator Cell F_F Comparator Cell Figure 12. MOS transistor implementation of TR_BME_FG Comparator Cell

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International Journal of VLSI design Communication Systems VLSICS Vol.5 No.5 October 2014 25 8. SIMULATION RESULT AND DISCUSSION Novel design of 2-bit 8-bit 64-bit and n-bit group-based reversible comparator is implemented in T-Spice and optimized the speed power for appropriate W/L ratio using 90nm technology node. Individual cell performance parameters analyse for reducing input voltage and finding power consumption delay etc. Figure 13. Simulation output of 1-bit comparator Figure 14. Power and delay Comparison at different input voltage of 1-bit comparator. 0.8 1 1.2 1.4 0 1 2 3 4 5 Power xE-06 Input Voltage V 0.8 1 1.2 1.4 0 0.5 1 1.5 2 2.5 Delay xE-08 Input Voltage V 0.6 0.6

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International Journal of VLSI design Communication Systems VLSICS Vol.5 No.5 October 2014 26 Figure 15. Input voltage versus Power delay product PDP of 1-bit Comparator. Figure 16. Simulation output of 2-bit comparator Figure 17. Power and delay Comparison at different Input voltage of 2-bit comparator. 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 0 0.5 1 1.5 2 2.5 3 3.5 4 Input Voltage versus Power delay product Input Voltage V PDP xE-14ws Power delay Product 0.8 1 1.2 1.4 1.6 0 1 2 3 4 5 6 7 8 9 x 10 -5 Input Voltage V Power xE-05 0.8 1 1.2 1.4 1.6 0 1 2 3 4 5 6 7 x 10 -8 Input Voltage V Delay xE-08

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International Journal of VLSI design Communication Systems VLSICS Vol.5 No.5 October 2014 27 Figure 18. Input voltage versus Power delay product PDP of 2-bit Comparator. Figure 19. Channel Length Variation versus power and delay of 2-bit Comparator Table 2. Comparison between anticipated and existing in terms of expertise of reversible gate 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 0 0.2 0.4 0.6 0.8 1 x 10 -12 Input Voltage V PDP xE-13 1 2 4 6 8 2 4 6 8 10 Channel Length Variation nm Maximum Power and Delay Variations versus Channel Length Variationu Maximum Power variation xE-05 Maximum Delay variation xE-08 RGate Gate can be used as n- bit comparator Single Gate can be used as Full subtractor Gate can be used as n-to-2 n decoder Anticipated Inventive Gate Y Y Y Available Circuit 4 Y N N Available Circuit 3 N N Y Available Circuit 12 N N N Available Circuit 13 N N N Available Circuit 15 N N N Available Circuit 6 Y N N Available Circuit 5 Y Y N

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International Journal of VLSI design Communication Systems VLSICS Vol.5 No.5 October 2014 28 Table 3. Comparison between anticipated and existing style comparator in terms of NOG GO CI power and delay NOG-number of gate GO-Garbage output CI-Constant input Table 4 Comparison between anticipated and existing style Comparator in terms of garbage output and constant input Methods NOG GO CI Power µW Delay ns Anticipated work 6+4n-1 1+4n-1 1+2n 85.81n – 78.98 115.010n – 100.854 Thaplial et al. 17 9n 6n −6 -- 268.23n −239.2 0.23 x log2n + 0.1 Vudadha et al. 18 4n −2 5n −4 -- 122.36n −60.36 0.09log2n + 0.2 Rangaraju et al. 7 7n −4 5n −4 -- 182.53n +76.55 0.2n − 0.16 Hafiz Md. Hasan Babu 4 3n 4n-3 3 117.76n −32.94 0.15n − 0.03

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International Journal of VLSI design Communication Systems VLSICS Vol.5 No.5 October 2014 29 9. CONCLUSION AND FUTURE WORK This paper is mainly focused on novel design of the reversible 4x4 inventive Gate. It utilized as 1-bit 2-bit 8-bit 32-bit and n-bit group-based binary comparator and n-to-2 n decoder. Moreover the low value styles of reversible parameter have been established for the proposed circuits. For example and n-to-2 n decoder uses at least 2 n + 1 reversible gates and its n garbage output: an n- bit comparator utilize 6+4 n - 1 number of reversible gate 1+4 n-1 garbage output. The proposed group- based comparator achieves the improvement of 19.87 in terms of garbage output and 31.57 in terms of constant input over the existing one 7. Simulation of the novel comparator circuits have shown that it works correctly and finding parameter power and delay. The proposed circuits will be useful for implementing the ALU and control unit of processor. ACKNOWLEDGMENT Authors would like to acknowledge Research Cum Teaching Fellowship through TEQIP-II provide by World Bank for the financial support for this work. REFERENCES 1 J R.Landauer “Irreversibility and Heat Generation in the Computational Process” IBM Journal of Research and Development pp: 183-191 1961. 2 C H Bennett “Logical Reversibility of Computation” IBM Journal of Research and Development vol. 17 no. 6 pp. 525-532November 1973. 3 Lafifa Jamal Md. Masbaul Alam Hafiz Md. Hasan Babu “An efficient approach to design a reversible control unit of a processor” Elsevier Sustainable Computing: Informatics and Systems pp: 286-294 2013 4 Hafiz Md. Hasan Babu Nazir Saleheen Lafifa Jamal Sheikh Muhammad SarwarTsutomu Sasao "Approach to design a compact reversible low power binary comparator" IET Computers Digital Techniques" Vol. 8 Iss. 3 pp. 129–139 doi: 10.1049/iet-cdt.2013.0066 2014 5 Ri-gui Zhou Man-qun Zhang QianWu •Yan-cheng Li "Optimization Approaches for Designing a Novel 4-Bit Reversible Comparator" Springer International jounal of theoretical physics DOI 10.1007/s10773-012-1360-y pp:559-575 2013 6 Farah Sharmin Rajib Kumar Mitra Rashida Hasan Anisur Rahman "Low cost reversible signed comparator" International Journal of VLSI design Communication Systems” Vol.4 No.5pp:19- 332013 7 Rangaraju H G Vinayak Hegdeb Raja K B Muralidhara K N "Design of Efficient Reversible Binary Comparator" Elsevier International Conference on Communication Technology and System Design Procedia Engineering pp:897-904 2012 8 Rangaraju H.G. Hegde V. Raja K.B. Muralidhara K.N. “Design of low power reversible binary comparator”. Proc. Engineering ScienceDirect 2011 9 Bahram Dehghan Abdolreza Roozbeh Jafar Zare "Design of Low Power Comparator Using DG Gate" Scientific research ciruits and systems doi.org/10.4236/cs.2013.51002pp: 7-12 2014 10 Pallavi Mall A.G.Rao H.P.Shukla "Novel Design of Four-Bit Reversible Numerical Comparator" International Journal of Advanced Research in Computer and Communication Engineering Vol. 2 Issue 4 pp:1808-1807 2013 11 Neeta Pandey Nalin Dadhich Mohd. Zubair Talha "Realization of 2-to-4 reversible decoder and its applications" International Conference on Signal Processing and Integrated Networks SPIN pp:349- 3532014 12 Md. M. H Azad Khan “Design of Full-adder With Reversible Gates”International Conference on Computer and Information TechnologyDhaka Bangladesh 2002 pp. 515-519

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International Journal of VLSI design Communication Systems VLSICS Vol.5 No.5 October 2014 30 13 Hafiz Md. Hasan Babu Md. Rafiqul Islam Syed Mostahed Ali Chowdhury and Ahsan Raja Chowdhury “Reversible Logic Synthesis for Minimization of Full Adder Circuit” Proceedings of the EuroMicro Symposium on Digital System DesignDSD’03 3-5 September 2003 14 Neeraj Kumar Misra Subodh Wairya Vinod Kumar Singh “Preternatural Low-Power Reversible Decoder Design in 90 nm Technology Node” International Journal of Scientific Engineering Research Volume 5 Issue 6 pp: 969-978 June 2014 15 J.W. Bruce M.A. ThorntonL. Shivakumariah P.S. Kokate and X.Li "Efficient Adder Circuits Based on a Conservative Logic Gate" Proceedings of the IEEE Computer Society Annual Symposium on VLSIISVLSI02April 2002 Pittsburgh PA USA pp 83-88. 16 Lafifa Jamal Md. Masbaul Alam Polash "On the Compact Designs of Low Power Reversible Decoders and Sequential Circuits" Springer LNCS7373 pp. 281–288 2012. 17 Himanshu Thapliyal Nagarajan Ranganathan and Ryan Ferreira "Design of a Comparator Tree Based on Reversible Logic" 10th IEEE International Conference on Nanotechnology Joint Symposium with Nano Korea pp:1113-1116 2010 18 Vudadha C.Phaneendra P.S.SreehariV.AhmedS.E.Muthukrishnan N.M.Srinivas “Design of prefix-based Optimal reversible comparator” IEEE Computer Society Annual Symp. On VLSI pp. 201–206 19 Nagamani A.N. Jayashree H.V. Bhagyalakshmi H.R.: ‘Novel low power comparator design using reversible logic gates’ Indian J. Comput. Sci. Eng.vol 2 4 pp. 566–574 2011 20 Morrison M. Lewandowski M. Ranganathan “Design of a tree-based comparator and memory unit based on a novel reversible logic structure” IEEE Computer Society Annual Symp. on VLSI pp. 331–336 2012 21 Neeraj Kumar Misra Subodh Wairya Vinod Kumar Singh “An Inventive Design of 44 Bit Reversible NS Gate” IEEE International Conference on Recent Advances and Innovation in Engineering ICRAIE-2014 pp: 1-6 2014 doi no. 10.1109/ICRAIE.2014.6909323

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