DNA Computing Units Based on Fractional Coding

Fractional encoding has been recently proposed as a promising convention to represent information in molecular computing systems. This paper presents new 2-input molecular computing units based on unipolar fractional representation. The units calculate simple computational equations that can be used for the computation of more complex functions. The design of these molecular computing units is inspired by fan-in 2 logic gates in the field of stochastic computing. Each computing unit consists of four chemical reactions with two reactants and one product. We design the DNA reactions implementing the chemical reactions of each unit based on the toehold-mediated DNA strand-displacement mechanism. Every unit is designed by four input strands and eight fuel gate strands of DNA. Since DNA molecules related to the input and output of the units have the same form of domain-toehold-domain-toehold, output molecules of each unit can be used as input for other units and this provides the cascading of the units for designing complex circuits. The whole DNA pathway for each unit is composed of twenty DNA reactions. The simulation results by Visual DSD show that the DNA implementations follow the theoretically expected computations of each unit with the maximum of 9.33% error.