South Asian Journal of Engineering and Technology Vol.2, No.20 (2016) 1–6

DNA Logic Gates to Design a 4*4 bit Carry Select Adder Circuit

Seeja V M Daniel Raj A Bannari Amman Institute of Technology Bannari Amman Institute of Technology Sathyamangalam, Erode Sathyamangalam, Erode [email protected] [email protected]

Abstract—The DNA molecule is indubitably the most economic limits. And also that has produced small, faster powerful medium known for DNA’s ability to code, store chips, beyond an certain limit, the number of silicon atoms in information as a means of data storage. But till now, DNA the insulating layer of a transistor is no longer sufficient to molecule has found little use in computing applications. For prevent the leakage of electron that causes the circuit to shorten initiating computing application with DNA molecule, it requires [1]. For overcome these limitations the scientists and to design DNA transistors which can be utilized to design basic technologists are looking for new materials, innovative gates to implement Boolean logic. Interestingly some recent structures and revolutionary ideas to realize reliable transistor researches have shown that it’s very much possible to design a like action in such tiny space [2].Most novel materials three terminal transistor like device architecture by controlling available today are at the first step, where researchers are the flow of RNA polymerase along DNA with specific integrases. trying to understand their properties and characteristics of Along with that, very recently, fundamental experimental designs for realizing various basic Boolean logic functions have been transistors fabricated using them. demonstrated successfully with DNA molecule. Present work Presently throughout the world several groups of scientists, adopted, modified and extended such DNA logic gate concept to researchers and technologists are trying to store, retrieve and execute design simulation of a 4*4 bit Carry select adder circuit. process signals using bio-chemical reactions with newer The timing diagram for input and sum output has been simulated biological materials [3-5]. In such context, with research it has and results have been presented. With present research, it has been proven that, the blueprint for life DNA, can also become been established that such DNA logic gate concept can be the templates for making a new generation of transistors, logic extended to complex circuits. At the same time, it has been also gates and subsequent computer chips [6]. In last decades lots of predicted that with the development of proper mathematical model for DNA transistor, a circuit simulator can be designed for research articles have been reported on experimental designing and simulating bioelectronics circuit in near future. realization of transistor like action and logic operation with DNAs [7-9]. Recently, Drew Endy et. al. at Stanford Keywords— DNA, RNA, Transistors, Logic Gates, Carry select University in California have designed a transistor like device adder Simulation that controls the movement of an enzyme called RNA polymerase along a strand of DNA with bacteriophage serine integrases [10]. They have also experimentally created logic I. INTRODUCTION gates that allow both information storage and logical The world of electronics starts with a material called operations with multiple transcriptors [10]. Such remarkable “semiconductor” which can be induced to conduct or stop the break through can be utilized to realize biochip and subsequent flow of electrons or holes. Si has been the dominant electronics biological computers which can be used to study and th material since the latter half of the 20 century. It must be clear reprogram living systems, monitor environments and improve that the successful development of Si devices took years and cellular therapeutics [9-10]. Till now most of the research decades. In conventional electronic circuits transistors are activities related to DNA logic gate realization are concentrated implemented to process, store and transfer signal or data with into intense experimental activities. But, along with such the flow of electrons or holes. Where as two or more transistors experimental ventures theoretical simulation is also important together form a logic gate, which allows a computer to manage to understand the operation and functionality of higher order mathematical operations. From the beginning to till date, the circuits with such DNA based logic gates. Under the present main aim of the electronics industry is to produce more work, based on DNA logic gates, a 4*4 bit Carry select adder powerful chips. In that process, designers have scale transistors has been logically realized with MATLAB Simulink. The input in size to produce smaller, faster, power efficient chip at lower and sum output for the DNA Carry select adder has been price [1]. The net result of this transistor scaling action is simulated and verified with timing diagrams. Such simulation because the transistor to reach the physical, technical and work will not only justify the applicability of such DNA logic

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South Asian Journal of Engineering and Technology Vol.2, No.20 (2016) 1–6 gates in complex circuit realization, it will also lead a step forward towards practical implementation of Bio-computers. Same time extension of present research with the development of proper mathematical model of DNA transistor will initiate the development of circuit simulator with DNA logic gates.

II. LOGICAL MODELING The RNA polymerase is an enzyme that also known as DNA dependent RNA polymerase and it produces primary transcript RNA chains using DNA genes as templates, a process called transcription [11].This produced primary transcript RNA can be reconfigured with a transistor like three terminal device model which can be named as transcriptor[10] The RNA synthesis follows after the attachment of RNA polymerase to a specific site, “promoter”, on the template DNA strand and the synthesis process continues until a termination sequence (“terminator”) is reached [12]. The flow of RNA polymerase along DNA strands between input and output induces an current called transcriptional current. The gate like control will be realized with independent chemical control signals (defined as “integrase”) which will regulate the flow of RNA polymerase to realize Boolean logic operation (“fig. 1”) [10].

Fig. 2. Logic control of RNA polymerase flow with integrase. Symbols: TE: Transcription Elements, RTE: Recombination sites for TE Fig. 1. Schematic for equivalent logic representation Under the present work, “Carry select adder”, a functional digital circuit built with two basic unit devices As shown in the “fig. 2”, the logic element will use (Full adders and multiplexer logic circuits), has been asymmetric transcription terminators as reversible check designed [13]. valves. A transcription terminator will be accommodating two Carry select adder (CSlA) circuit architecture consists opposing DNA recombination sites named as Transcription of independent generation of sum and carry i.e Cin=1 and Elements (TEs, represented with dark green and dark blue solid Cin=0 are executed parallelly. Depending upon Cin. The triangles) which will normally disrupt RNA polymerase flow. The input integrase which is recombinases (genetic external multiplexers select the carry to be propagated to recombination enzymes) will catalyze unidirectional inversion next stage. Further, based on the carry input, the sum will of DNA within opposing recombination sites [10]. This will be selected. The Simulink model of CSlA is shown below. modify TEs (represented with partially dark green-blue and The Carry select adder adds two four-bit binary numbers partially dark blue-green solid triangles) and invert of the and the outputs will be produced as the sum of the two transcription terminator to provide of DNA recombination sites four bit input as shown in “fig. 3”. and will allow RNA polymerase flow. Every opposing recombination sites (TEs) will be recognized by independent integrases which will provide independent control over the orientation or presence of one or more terminators.

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South Asian Journal of Engineering and Technology Vol.2, No.20 (2016) 1–6

Fig. 3. Schematic for logical carry select adder circuit Fig. 5. Schematic for logical DNA EXOR showing transcription continuation with presence of integrase 1 (=1). So to realize a Carry select adder circuit with DNA logic, the basic DNA EXOR, AND and OR gates have to be designed first. Then with the basic logic gates the half adder [13], full B. Implementing AND Logic adder and multiplexer circuits also designed. A transcriptor AND logic element requires two asymmetric transcription terminators with two pairs of opposing A. Implementing EXOR Logic recombination sites (Transcription Elements) associated with As shown in Fig. 4, a transcriptor EXOR logic element each transcription terminator, as shown in Fig. 5. The requires one asymmetric transcription terminator with two transcription current will flow only when both the intergaces pairs of opposing recombination sites (TEs) recognized by will present but no transcription current flow if only one independent integrases. When none of the integrase is present, integrase is present as shown in “fig 6”. the terminator will block the transcription as shown in fig 4.

Fig. 6. Schematic for logical representation of AND showing blocked Fig. 4. Schematic for logical DNA EXOR showing blocked transcription with transcription with presence of intergace 1 and absence of intergace 2. absence of intergace 1 and 2. Symbols: TEa and RTEa are associated with integrase 1; TEb and RTEb are associated with integrase 2, respectively.

B. Implementing OR Logic Presence of any one of the integrase will flip the terminator A transcriptor OR logic element requires only one and will modify a pair of transcription element which will asymmetric transcription terminator with two pairs of allow the transcription current to flow (“fig. 5”). Whereas the opposing recombination sites (Transcription Elements) presence of both the integrases will invert the terminator twice associated with transcription terminator. The transcription which will restore the terminator’s original orientation and will current will flow if any one of the integrases will present but block transcription again. no transcription current flow when only both the integrase is absent as shown in “fig 7”.

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South Asian Journal of Engineering and Technology Vol.2, No.20 (2016) 1–6

every block is fitted with logical function to replicate transcriptor and transcription elements. Whereas the pulse source of variable widths have been considered for replicating integrase a, b and a unit step function has been selected to replicate RNA polymerase input. Where in the above Simulink model dark green block for full adder logic, light blue for multiplexer logic. The top side represent the input section. Red color for the input RNA polymerase, dark blue for integrase a (a0,a1,a2 and a3), integrase b (b0,b1,b2 and b3) and orange for carry inputs.

Fig. 7. Schematic for logical DNA OR showing transcription continuation with presence of integrase 1 (=1).

With further extension of this concept, other Boolean logics like NAND, NOR, NOT can be also implemented with DNA logic [9-10].

III. RESULTS AND DISCUSSION Under the present work, a 4*4 bit Carry select adder circuit has been logically design and implemented with MATLAB Simulink and the timing diagram for input and sum output has been successfully simulated. The Simulink block diagram of the Carry select adder has been presented in “fig. 8”. Where RNA polymerase has been considered as input signal and two integrase a, b of 4 bit binary will from the logic inputs for the Carry select adder.

Fig. 9. With time the integrase a0,a1,a2,a3,b0,b1,b2,b3 and RNA given as top to bottom.

Fig. 8. Simulink block diagram of Carry select adder with 8 full adders and 5 multiplexer circuits.

To implement the Carry select adder in Simulink user Fig. 10. With time the 5 bit sum s0,s1,s2,s3 and carry output are shown from defined function block has been selected from library and bottom to top.

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South Asian Journal of Engineering and Technology Vol.2, No.20 (2016) 1–6

signal pulses were sufficient to activate integrase-mediated Correlation of output with control signal integrase a, switching. So the each and every gates present in the circuit integrase b, and input signal (RNA polymerase) has requires 15 min for their switching. For the half adder the successfully implemented Wallace tree multiplier circuit as switching time is 15.Whereas in the full adder the time shown in “fig. 9” and “fig. 10”. required is about 45 min. The delays for each logic circuit present in the adder circuit is given in Table III, from that the propagation delay for the proposed Carry select adder is calculated. TALE I

Time unit Integrase a Integrase b Output sum IV. CONCLUSION (a3 a2 a1 a0) (b3 b2 b1 b0) (c s3 s2 s1 s0) 2 1101 1101 11010 6 1111 0111 10110 Under the present work the DNA logic gate design concepts Fig.11. Truth table for 4*4 bit Wallace tree multiplier has been theoretically investigated in detail. The logical design concepts of EXOR, AND and OR gate have been TABLE II implemented with proper understanding and explanations. Finally a 4*4 bit Carry select adder has been logically Time Integrase a Integrase b Change in Sum(error in %) designed with DNA based Full adder and multiplexer circuit unit (a3 a2 a1 a0) (b3 b2 b1 b0) output s (c s3 s2 s1 with MATLAB Simulink model. The timing diagrams for the s0) C s3 s2 s1 s0 summed output, logic inputs and input signal are simulated. 2 0 1, 0 1, 1 1, 1 1, 11010 15 15 15 The digitization error in percentage has also been 0 0, 0 1. 0 0, 0 1 6 0 1, 0 1, 0 0, 0 1, 10110 15 15 15 approximated and presented for different input combinations 0 1, 0 1. 0 1, 0 1. for the carry select adder circuit. And also the propagation Fig. 12. Error percentage table for wallace tree multiplier delay for entire circuit is calculated and presented for possible

paths between input to output. Such block level design of TABLE III DNA Carry select adder circuit will provide valuable

Sl no. Logic circuits Delay understanding about the DNA based logic circuit design. Not 1 AND 15 only that such block level design can be added with proper 2 XOR 15 mathematical model of DNA transistor which will initiate the 3 Full Adder 45 4 Multiplexer 45 development of future bioelectronics circuit simulators. Total propagation delay for the Adder circuit 4hr 30min Fig.13. Delay table for the Wallace tree multiplier circuit REFERENCES

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