# Transforming Group Codes in Mealy Finite State Machines with Composite State Codes
## 7 Conclusions  
One of the basic problems associated with LUT-based FSM design is the problem of improving the temporal characteristics of the produced circuits. Under certain conditions, the best spatial characteristics are provided if FSM states are encoded by composite state codes [11]. This method is based on finding a partition of the set of states according to the minimum number of groups of compatible states. In the composite state codes proposed in article [11], there was the minimum possible number of bits in the group codes. Within each group, states were encoded by partial maximum binary codes. To increase the maximum operating frequency of CSC-based FSM circuits, we propose encoding groups using one-hot codes. As the conducted experiments show, the proposed method provides a reduction in the value of the cycle time compared with that of the equivalent CSC-based FSMs. This reduction is possible for rather complex FSMs for which the total number of inputs and state variables is at least twice the number of inputs of the base LUT. For example, for FSMs whose circuits are implemented using six-input LUTs, an improvement in the temporal characteristics is possible if \(L+R>12\). The proposed method has the following positive feature: an increase in performance (an increase in the maximum operating frequency) is accompanied by a slight decrease in the LUT count. As shown through the experiments, the results of which were given in the previous section, the proposed method can only be applied to an FSM for which condition (28) is met. If the sum of digits of codes with the appropriate number of logical conditions does \begin{table}
\begin{tabular}{l r r r r r} \hline
**BM** & **MB** & **OH** & **JEDI** & **\(\mathbf{U_{2}}\)** & **\(\mathbf{U_{3}}\)** & **L + R** \\ \hline ex1 & 46,376 & 52,948 & 29,966 & 14,481 & 12,957 & 16 \\ \hline kirkman & 29,707 & 37,662 & 24,891 & 13,513 & 11,980 & 18 \\ planet & 98,711 & 98,711 & 47,024 & 26,878 & 23,914 & 14 \\ planet1 & 98,711 & 98,711 & 47,024 & 26,878 & 23,914 & 14 \\ \hline pma & 64,304 & 64,304 & 50,639 & 29,373 & 25,582 & 14 \\ \hline s1 & 44,396 & 72,874 & 38,814 & 23,281 & 20,288 & 14 \\ \hline s1488 & 89,531 & 99,288 & 68,711 & 38,138 & 35,427 & 15 \\ \hline s1494 & 84,343 & 90,566 & 66,934 & 37,572 & 34,259 & 15 \\ \hline s1a & 31,949 & 45,918 & 25,418 & 19,441 & 17,006 & 15 \\ \hline s510 & 27,019 & 27,019 & 17,639 & 11,910 & 10,441 & 27 \\ \hline s820 & 57,895 & 53,539 & 38,509 & 21,213 & 16,960 & 25 \\ \hline s832 & 54,904 & 51,556 & 35,677 & 22,763 & 20,624 & 25 \\ \hline sand & 113,823 & 113,823 & 89,891 & 40,260 & 35,927 & 18 \\ \hline styr & 67,582 & 92,365 & 55,617 & 26,402 & 24,183 & 16 \\ \hline tma & 27,459 & 26,387 & 23,760 & 11,027 & 10,222 & 13 \\ \hline Total & 9367 & 10,257 & 6605 & 3631 & 3237 & \\ \hline Percentage, \% & 28,939 & 31,687 & 20,406 & 11,219 & 10,000 & \\ \hline \end{tabular}
\end{table} 
Table 11: Results of experiments (area–time products). not exceed twice the number of LUT inputs, then the use of this method does not make sense. In this case, it is advisable to use the other methods of state coding discussed in this article. An analysis of the tables containing the results of the studies shows that the improvements from the application of the proposed method increase as the value of the parameter \(L+R\) increases. So, the proposed state assignment method allows for an increase in the FSM performance without increasing the amount of internal chip resources used. The results of the investigations show that the proposed method can be used for designing rather complex FSMs. Conceptualization, A.B., L.T. and K.M. ; methodology, A.B., L.T. and K.M. ; formal analysis, A.B., L.T. and K.M. ; writing-original draft preparation, A.B., L.T. and K.M. ; writing--review and editing, A.B., L.T. and K.M. ; supervision, A.B. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. The data presented in this study are available in the article.