Author : Ravish Aradhya H V, Praveen Kumar B V, Muralidhara K N

International Journal of Scientific & Engineering Research Volume 2, Issue 9, September-2011

ISSN 2229-5518

Download Full Paper : PDF**Abstract—**Technology advances in VLSI designs offer exponentially shrinking device dimensions and exponentially growing circuit complexities. However, device scaling is critically limited by the power dissipation; demanding for better power optimizations methods. Reversible Logic is becoming more and more prominent special optimization technique having its applications in Low Power CMOS designs, Quantum Computing and Nanotechnology. ALU is a fundamental building block of a central processing unit (CPU) in any computing system; reversible arithmetic unit has a high power optimization on the offer. By using suitable control logic to one of the input variables of parallel adder, various arithmetic operations can be realized. In this paper, as a part of ALU design, a Reversible low power control unit for arithmetic operations is proposed. In our design, the full Adders are realized using synthesizable, low quantum cost, low garbage output Peres gates. In this paper data transfer, addition, subtraction, increment, decrement and many other Arithmetic operations are realized using reversible gates.

**Index Terms—** Fredkin Gate, Garbage output, Low Power, Power Optimization, Quantum Cost, Reversible control Unit, Reversible Logic.

**1. INTRODUCTION**Design of a control unit for any computing unit is the toughest part and involves more critical constraints. Power consumption is an important issue in modern day VLSI designs. The advancement in VLSI designs and particularly portable device technologies and increasingly high computation requirements, lead to the design of faster, smaller and more complex electronic Systems. The advent of multi-giga-hertz processors, high-end electronic gadgets bring with them an increase in system complexity, high density packages and a concern on power consumption. Power optimization can be done at various abstraction levels in CMOS VLSI design. At the Device (Technology) level, techniques such as VT reduction, multi-threshold voltages, gate oxide thickness, length and width variations are more common. At Circuit level, techniques such as use of alternate devices, network re-structuring, at Logic level, techniques such as use of alternate logic styles, energy recovery methods are common. At Architecture (System) level and Algorithmic level, techniques such as use of parallel structures, pipelining, state machine encoding, alternate encoding methods, etc are more common. Ref. [23] offers one such method at circuit and logic level, the energy recovery method, which employs reversible logic concepts.

In 1973, C. H. Bennett [1,3] concluded that no energy would be dissipated from a system as long as the system

Ravish Aradhya H V is an associate professor and Praveen Kumar B V is a Masters student in Electronics and Communication Engineering Department, R V college of Engineering, Bangalore 560 059, India. E-mail:

ravisharadhya@rvce.edu.inMuralidhara K N is professor and Head in Electronics and Communication Engineering Department, P E S college of Engineering, Mandya 571 401, India. was able to return to its initial state from its final state regardless of what occurred in between. It made clear that, for power not to be dissipated in the arbitrary circuit, it must be built from reversible gate. Reversible circuits are of particular interest in low power CMOS VLSI design.

**2. REVERSIBLE GATES**The basic and simplest Reversible gate is conventional NOT gate and is a 1*1 gate. Controlled NOT (CNOT) gate is an example for a Reversible 2*2 gate. There are many 3*3 Reversible gates such as FG, TG, PG and Fredkin Gate. The Quantum Cost of 1*1 Reversible gates is zero and Quantum Cost of 2*2 Reversible gates is one. Any Reversible gate is realized by using 1*1 NOT gates and 2*2 Reversible gates, such as V, V+ (V is square root of NOT gate and V+ is its hermitian) and FG gate which is also known as CNOT gate. The V and V+ Quantum gates have the property given in the Equations 1, 2 and 3.

V * V = NOT ……………… (1)

V * V+ = V+ * V = I ……….. (2)

V+ * V+ = NOT ……………. (3)

The Quantum Cost of a Reversible gate is calculated by counting the number of V, V+ and CNOT gates. There are several popular Reversible gates among the designers; Fredkin and Peres being emphasized here.

Feynman / CNOT Gate: The Reversible 2*2 gate with Quantum Cost of one having mapping input (A, B) to output (P = A, Q = AB) is the basic reversible gate (However, the basic Reversible 1*1 gate without any control input is a CMOS NOT Gate and its Quantum Cost is zero).

Toffoli gate: The Reversible 3*3 gate with three inputs and three outputs where the inputs (A, B, C) are mapped to the outputs (P=A, Q=B, R=A.BC) has Quantum Cost of 5 and requires 2V, 1 V+ and 2 CNOT gates.

Peres Gate: The three inputs and three outputs i.e., 3*3 reversible gate having inputs (A, B, C) mapping to outputs (P = A, Q = AÅ B, R = (A.B) Å C).

Since it requires 2 V+, 1 V and 1 CNOT gate, it has the Quantum cost of 4. The Peres gate and its Quantum implementation are shown in the Fig. 1.

Fredkin Gate: Reversible 3*3 gate maps inputs (A, B, C) to outputs (P=A, Q=A'B+AC, R=AB+A'C) having Quantum cost of 5 and it requires two dotted rectangles, is equivalent to a 2*2 Feynman gate with Quantum cost of each dotted rectangle is 1, 1 V and 2 CNOT gates. Fredkin gate and its Quantum implementations are shown in Fig. 2.

**3. LITERATURE SURVEY**R. Landauer’s [2] showed, the amount of energy (heat) dissipated for every irreversible bit operation is given by KT ln2, where K is the Boltzmann’s constant (1.3807×10-23 JK-1) and T is the operating temperature. At room temperature (300 K), KT ln2 is approximately 2.8×10-21 J, which is small but not negligible. He also showed that only the logically irreversible steps in a computation carry an unavoidable energy penalty. If we could compute entirely with reversible operations, there would be no lower limit on energy consumption.

Bennett showed that kTln2 energy dissipation would not occur, if a computation is carried out in a reversible way [1], since the amount of energy dissipated in a system bears a direct relationship to the number of bits erased during computation. He presented his idea in terms of a Turing machine, the abstract model of a computer that reads, writes and erases symbols on a tape. Erasures make the standard Turing machine irreversible, so Bennett added a second tape, called the history tape, where the machine keeps notes about erased or overwritten data. At the end of a computation, the final answer can be copied onto yet another tape for safekeeping. Then the machine is put in reverse gear, and with the help of the history tape, all the operations are undone, one by one, until the system returns to its initial condition. Yingtao Jiang, Abdulkarim Al-Sheraidah, Yuke Wang, Edwin Sha and Jin-Gyun Chung [12] have proposed low-power multiplexer-based 1-bit full adder that uses only 12 transistors and the new adder has more than 26% in power savings over conventional 28-transistor CMOS adder. Also, it consumes 23% less power than another 10-transistor adder and is 64% faster. Anantha P. Chandrakasan, Samuel Sheng, and Robert W. Brodersen [4] have given techniques for low-power operations, which can use the lowest possible supply voltage coupled with architectural, logic style, circuit and technology optimizations. Dmitri Maslov and Gerhard W. Dueck [13] introduced a synthesis model and a synthesis procedure which allow us to minimize the number of garbage outputs in reversible circuit and also showed that the new gates differ only marginally from the generalized Toffoli gates. Alberto Nannarelli and Tomás Lang [14] have illustrated some techniques for dividers realized in CMOS technology and energy dissipation reduction is carried out at different levels of abstraction: from the algorithm level down to the implementation or gate level. They also described the use of techniques such as switching-off non- active blocks, re-timing, dual voltage, and equalizing the paths to reduce glitches. Vivek V. Shende, Aditya K. Prasad, Igor L. Markov, and John P. Hayes [15] have synthesized oracle circuits for Grover’s search algorithm and shown a significant improvement over previously proposed synthesis algorithms and also showed constructively that every even permutation can be implemented without temporary storage using NOT, CNOT and TOFFOLI gates. William C. Athas, Lars “J” ,Svensson, Jeffrey G. koller, Nestoras Tzartzanis, and Eric Ying – Chin Chou[16] have showed that circuit energy can be conserved rather than dissipated as heat. Yvan Van Rentergem and Alexis De Vos [5] presented four designs for Reversible full-adder circuits and the implementation of these logic circuits into electronic circuitry based on CMOS technology and pass-transistor design. Himanshu Thapliyal and Srinivas [11] proposed a 3x3 Reversible TKS gate with two of its outputs working as 2:1 multiplexer. The gate used to design a Reversible half adder and further used to design multiplexer based Reversible full adder. Rekha James et al., [17] proposed an implementation of Binary Coded Decimal adder in Reversible logic, which is basis of ALU for reversible CPU. Majid Mohammadi et al., [6] proposed a synthesis method to realize a Reversible Binary Coded Decimal adder/subtractor circuit. Genetic algorithms and don’t care concepts used to design and optimize all parts of a Binary Coded Decimal adder circuit in terms of number of garbage inputs/outputs and quantum cost. Lihui Ni et al., [18] described general approach to construct the Reversible full adder and can be extended to a variety of Reversible full adders with only two Reversible gates. Hasan, H.B., R. Islam, A.R. chowdhury and S.M.A chowdhury [20], proposed full adder circuit using Toffoli, Khan and Feynman gates with gates cost equal to 3, 2 garbage outputs and 1 constant input. Similarly, Perkowski M., L. Jozwiak, P. Kerntopf, A. Misohchenko and A. Al-Rabadi [21] proposed another full adder with only Toffoli and Feynman gates, with gates cost equal to 4, 2 garbage outputs and 1 constant input. Azad khan, M.H [24] proposed full adder with only Kahn and Feynman gates, with gates cost equal to 3, 3 garbage outputs and 2 constant input. Bruce, J.W., M.A. Thornton, L. shivakuamaraiah, P.S. kokate and X. Li [25], used only Fredkin gates to construct full adder with gates cost equal to 4, 3 garbage outputs and 2 constant input. Rangaraju H G [10] discussed various adder/subtractor circuit designs and showed that design III is good and optimized. Md. Saiful Islam, Muhammad Mahbubur Rahman, Zerina begum, and Mohd. Zulfiquar Hafiz [7], designed full adder circuit using IG gates and MIG gates with constant inputs of 2 and Garbage output of 3, and designed Fault Tolerant Reversible Carry Look-Ahead and Carry-Skip Adders. Bart Desoete, Alexis De Vos[8] used generalized Feynman’s three gates to arbitrary control gates and designed reversible 4-bit carry-look-ahead adder. In Ref. [22] design of complete processing unit is discussed using conventional logic. Same logic discussed in [22] is being used in our work. In Ref. [23] various low power VLSI techniques for power reduction and optimization are discussed. Saiful Islam and Rafiqul Islam [9], came up with good design for full adder using Peres gate with gates cost equal to 2, 2 garbage outputs and 1 constant input and this design is used in our implementation of arithmetic unit.

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