# Prospects for the Use of Quasi-Mersen Numbers in the Design of Parallel-Serial Processors
## 3 Discussion  
The proposed scheme for the adder modulo a quasi-Mersen number allows for the future to implementation of a processor that performs serial-parallel calculations due to the built in algorithm, built on a very specific RNS. As outlined in Section 2, the fact that this RNS is built on quasi-Mersen numbers allows to implement a relatively simple (compared with existing analogs) adder scheme. The basis of this processor is a set of adders in the fields \(GF\left(2^{k}+1\right)\), each of which operates independently. The simplest architecture of this processor can be implemented by analogy with existing processors, in which the basic operation is addition. The difference is that all numbers inputted into the calculator are initially converted into a format corresponding to the RNS of the proposed type. Consequently, further operations with each \"component\" of each number are carried out independently. Specifically, this means that the performance of such a processor is minimally affected by the units that provide the reduction of a number to a set of numbers modulo the first quasi-Mersenne numbers (the same applies to the inverse operation). Performance is determined solely by the adder itself, and the limiting factor (in terms of calculation speed, etc.) is associated with the adder containing the maximum number of elements (i.e., the adder modulo 257). This number corresponds to an 8-bit adder, while the adder as a whole corresponds to a 16-bit adder in terms of performance. The prospects for the widespread use of a processor of this type may still be debatable; however, it is possible to indicate a very specific range of problems for which this processor is either optimal or close to optimal. For example, this applies to the calculation of partial convolutions, considered in [19]. There is no need to emphasize that the development of devices that calculate digital convolutions is becoming increasingly relevant. In particular, this is due to the increasingly widespread use of convolutional neural networks [36; 37; 38], which are used, among other things, for primary data processing by onboard computing systems installed on devices for various purposes. In particular, the development of onboard computing systems that perform primary image processing during remote sensing of the Earth is relevant. Specifically, it is necessary to exclude the transmission of images in cases where the surface is covered by cloud cover [39; 40]. Figure 6: ModelSim testbench result (mod17). To solve such problems, it is advisable to use a processor of the proposed type precisely because it operates independently with different components of an integer. Consequently, it can be used both for standard calculations and for calculations oriented towards the use of partial convolutions, as described in [19], which is specially designed for the implementation of convolutional neural network algorithms. Examples from other fields can also be provided, in which the proposed approach may be in demand. This applies, in particular, to the development of new measuring devices using the Fourier-Galois transform. An example of such a device (a viscometer), using the GF(31) field, was considered in [41]. Other devices of this type, in which the electronic unit is significantly modernized [42], could be oriented towards other fields. However, the most important thing is that, in this case, the range of numbers in which the calculations are performed remains limited. Another non-trivial field of application for the developed approach in the future may be electronics implemented on a non-standard element base. The search for such an element base is currently being pursued very actively (for example, this concerns the development of neuromorphic materials [43; 44; 45], optical computers [46; 47], etc.). Promising neuromorphic materials are very diverse. In particular, it has been proposed to use organic electronics for this purpose [48; 49], including those that use organic transistor [50] and optoelectronic elements [51].