# Conversion between Number Systems in Membrane Computing
###### Abstract  
The number system is the representation method of numbers, and number system conversion is the most basic function of a computing system. The decimal system is the most commonly used number system; however, it may not necessarily be the most suitable number system in a computing system. This paper investigates the conversion methods between different number systems and designs corresponding cells, such as P systems, to implement them. The P systems we designed include \(\Pi_{10,2}\) and \(\Pi_{2,10}\) to implement conversion between decimal and binary, \(\Pi_{10,0}\) and \(\Pi_{m,10}\) to implement conversion between decimal and m-base. The operation process of each P system was explained through examples, and their feasibility and effectiveness were verified through simulation software, UPSimulator. number system conversion; cell-like P systems; membrane computing; UPSimulator +
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within the membrane structure. In order to achieve a flow of objects between membranes, such as the result of computation within one membrane structure as the initial object of a rule execution within another membrane structure, a mechanism is needed that allows the flow of substances between membrane structures, and thus the transit P system is proposed [5]. The active membrane P system [6; 7; 8] can treat not only elements in multiple sets but also membranes. It can dissolve, generate, split, and merge membranes. When the membrane is dissolved, the objects inside the membrane will be released into the outer membrane, and the rules inside the membrane will not exist. When membranes merge, the objects and rules in each of the merged membranes will exist simultaneously within a single membrane structure. Numerical computation as a field of membrane computing research and application has yielded some results: Reference [9] designed four basic arithmetic operators based on neural P systems for addition, subtraction, multiplication, and division, achieving basic arithmetic operations. Reference [10] designs the implementation of the corresponding spiking neural P systems, including two's complement, addition /subtraction on signed integers, and multiplication on two arbitrary natural numbers. In reference [11], the author proposed a complete arithmetic calculator implemented by spiking neural P systems and also gave its application in information fusion. Reference [12] implements arithmetic operations for cell-like P systems with multilayer cell membranes. Reference [13] further improves on reference [12] by using a single membrane structure to achieve arithmetic operations. A new arithmetic P system is proposed in reference [14], which can perform four basic operations. By directly placing the digits of decimal integers into the layered membrane, the number of membranes is reduced, thereby reducing complexity. In [15], multimembrane P systems are constructed for signed arithmetic operations. Reference [16] implements an arithmetic operation on a rational number field, and reference [17] introduces the method of unsigned fraction reduction. In addition, in order to simulate hybrid P systems, a simulator called UPSimulator was proposed in reference [18], which can serve as a development library for P system models. This model processes objects in the region defined by membranes and supports complex evolutionary rules and structures in different types of P systems. This simulator serves as the main tool for verifying the correctness of the membrane rules in Section 5. Modern computers are still based on [PERSON]'s architecture, a feature of which is that data and instructions are represented in binary form. The reasons for using binary are as follows: (1) Binary only needs two states to represent numbers. It is easy to implement binary numbers '0' and '1' using bistable circuits in computers.