# Improving Hardware in LUT-Based Mealy FSMs
## 6 Experimental Results
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Benchmark** & **Auto [13]** & **One-Hot [13]** & **JEDI [14]** & **U\({}_{2}\) [14]** & **Our Approach** \\ \hline bbara & 193.39 & 193.39 & 212.21 & 202.23 & 201.12 \\ \hline bbsse & 157.06 & 169.12 & 182.34 & 181.23 & 178.64 \\ \hline beecount & 166.61 & 166.61 & 187.32 & 185.14 & 183.72 \\ \hline cse & 146.43 & 163.64 & 178.12 & 175.18 & 172.42 \\ \hline dk14 & 191.64 & 172.65 & 193.85 & 190.18 & 188.86 \\ \hline dk15 & 192.53 & 185.36 & 194.87 & 192.23 & 191.48 \\ \hline dk16 & 169.72 & 174.79 & 197.13 & 194.34 & 192.83 \\ \hline donfile & 184.03 & 184 & 203.65 & 200.92 & 198.47 \\ \hline ex2 & 198.57 & 198.57 & 200.14 & 198.32 & 197.26 \\ \hline ex4 & 180.96 & 177.71 & 192.83 & 190.14 & 188.32 \\ \hline ex6 & 169.57 & 163.8 & 176.59 & 171.27 & 170.18 \\ \hline ex7 & 200.04 & 200.84 & 200.6 & 198.14 & 197.38 \\ \hline keyb & 156.45 & 143.47 & 168.43 & 162.01 & 161.25 \\ \hline mark1 & 162.39 & 162.39 & 176.18 & 170.18 & 168.04 \\ \hline opus & 166.2 & 166.2 & 178.32 & 175.29 & 173.41 \\ \hline s27 & 198.73 & 191.5 & 199.13 & 196.13 & 194.17 \\ \hline s386 & 168.15 & 173.46 & 179.15 & 176.85 & 174.62 \\ \hline s8 & 180.02 & 178.95 & 181.23 & 178.23 & 176.22 \\ \hline sse & 157.06 & 169.12 & 174.63 & 170.12 & 167.43 \\ \hline Total & 3339.55 & 3335.57 & 3576.72 & 3508.13 & 3475.82 \\ \hline Percentage,\% & 96.08 & 95.96 & 102.90 & 100.93 & 100.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Experimental results (the maximum operating frequency for G1). As follows from Table 8, the \(U_{3}\)-based FSMs require fewer LUTs than do the other investigated methods. Our approach produces circuits with 46.52% less 6-LUTs than for equivalent auto-based FSMs; 70.50% less 6-LUTs than for equivalent one-hot-based FSMs; and 20.66% less 6-LUTs than for equivalent JEDI-based FSMs. Additionally, our approach provides the gain (7.21%) respectively to equivalent \(U_{2}\)-based FSMs. However, the amount of gain (or loss) depends on each group that a particular benchmark belongs to. As follows from Table 9, our approach loses compared to all other investigated methods. There are the following losses: 30.11% relative to auto-based FSMs; 4.44% relative to one-hot-based FSMs; 32.22% relative to JEDI-based FSMs (7.58% loss); and 1.11% relative to \(U_{2}\)-based FSMs. So, it does not make sense to use the \(U_{3}\)-based FSMs to implement the circuits for FSMs of the group G0. Let us explain the reasons for these losses. Comparing the results for group G0 shows that both multilevel approaches (\(U_{2}\) and \(U_{3}\)) lose out to the other methods. For FSM \(U_{2}\), the loss is 30% compared to auto-based FSMs, 3.43% compared to one-hot-based FSMs, and 31.11% compared to JEDI-based FSMs. We explain this by the fact that condition (4) holds for benchmarks of G0. In this case, only a single LUT is needed to implement any function from SBFs (2) and (3). So, there is no need in the encoding of COs. However, as follows from Figures 4 and 6, this method is always used in both multi-level FSMs \(U_{2}\) and \(U_{3}\). Due to it, for the group G0, the multilevel FSMs have higher LUT counts than for the other investigated design methods.