# Transforming Group Codes in Mealy Finite State Machines with Composite State Codes
## 6 Experimental Results
As follows from Table 8, our method provided an improvement of around 19%. As we compare the results for each benchmark, we can make the following conclusion: the improvement achieved by replacing composite state codes with mixed CSCs increased with the growth of the value \(L+R\). We think that this phenomenon was related to the difference in the number of CLBs connected in series in the circuit creating the input memory functions and outputs of Mealy FSMs. As the value of \(L+R\) increased, the number of consecutive CLBs grew faster for CSC-based FSMs than for the equivalent MCSC-based FSMs. Using the values for the cycle time allowed us to create Table 9. This table shows the values of the maximum operating frequencies. As follows from Table 9, the proposed method produced FPGA-based FSM circuits with higher frequencies than the other studied FSMs. As can be seen from Table 9, \(U_{3}\)-based FSMs achieved the following improvements in the frequency: (1) 45.2% compared with Auto-based FSMs; (2) 55.49% compared with OHC-based FSMs; (3) 37.44% compared with JEDI-based FSMs; and (4) 7.89% compared with \(U_{2}\)-based FSMs. The reasons for this state of affairs have already been considered in the analysis of the data from Table 8. We will not repeat them. The main goal of the proposed approach is to improve the temporal characteristics of LUT-based FSM circuits in relation to the circuits of the equivalent CSC-based FSMs, but sometimes, it is very important that an increase in the frequency does not result \begin{table}
\begin{tabular}{l c c c c c c} \hline
**BM** & **MB** & **OH** & **JEDI** & \(\mathbf{U_{2}}\) & \(\mathbf{U_{3}}\) & **L + R** \\ \hline ex1 & 15,094 & 13,976 & 17,687 & 27,623 & 29,327 & 16 \\ \hline kirkman & 14,138 & 15,400 & 15,668 & 22,941 & 25,042 & 18 \\ planet & 13,271 & 13,271 & 18,714 & 28,648 & 30,108 & 14 \\ \hline planet1 & 13,271 & 13,271 & 18,714 & 28,648 & 30,108 & 14 \\ \hline pma & 14,618 & 14,618 & 16,983 & 24,512 & 26,972 & 14 \\ \hline s1 & 14,641 & 13,585 & 15,716 & 23,624 & 25,631 & 14 \\ \hline s1488 & 13,850 & 13,194 & 15,718 & 22,812 & 23,711 & 15 \\ \hline s1494 & 14,939 & 14,575 & 16,434 & 22,623 & 23,935 & 15 \\ \hline s1a & 15,337 & 17,640 & 16,917 & 22,118 & 23,521 & 15 \\ \hline s510 & 17,765 & 17,765 & 18,142 & 21,831 & 26,817 & 27 \\ \hline s820 & 15,200 & 15,316 & 17,658 & 22,628 & 27,123 & 25 \\ \hline s832 & 14,571 & 15,323 & 17,378 & 21,965 & 25,213 & 25 \\ \hline sand & 11,597 & 11,597 & 12,682 & 22,603 & 24,216 & 18 \\ \hline styr & 13,761 & 12,992 & 14,564 & 26,892 & 28,532 & 16 \\ \hline tma & 16,388 & 14,780 & 16,414 & 28,114 & 28,371 & 13 \\ \hline Total & 218,441 & 217,303 & 249,389 & 367,582 & 398,627 & \\ \hline Percentage, \% & 5480 & 5451 & 6256 & 9221 & 100\% & \\ \hline \end{tabular}
\end{table} 
Table 9: Results of experiments (maximum operating frequency, MHz). in a significant deterioration of the spatial characteristics. These characteristics depend significantly on the number of LUTs used (LUT count) [12]. A comparison of the values of the LUT counts for FSM circuits based on various state assignment methods is shown in Table 10.  
As follows from Table 10, the proposed approach led to the creation of FSM circuits that required fewer LUTs than the other investigated methods. Our method had an average improvement of (1) 55.06% compared with Auto-based FSMs, (2) 68.35% compared with OHC-based FSMs, (3) 26.12% compared with JEDI-based FSMs, and (4) 4% compared with FSMs based on composite state codes. Sometimes, it is very important to reach a balance between the spatial and temporal characteristics of FSM circuits [19]. This balance can be estimated using some integral evaluations of the quality of a digital circuit. One of the main integral evaluations involves the product of the area occupied by a circuit and its performance (area-time product) [12]. In the case of LUT-based circuits, the area is estimated using a characteristic such as the LUT count [12]. Obviously, the performance is represented by the value of the cycle time.