# Improving Hardware in LUT-Based Mealy FSMs
## 6 Experimental Results
As follows from the research results, the implementation of systems (5) and (10) requires more internal resources than the implementation of the system (7). This advantage of FSMs \(U_{3}\) in relation to FSMs \(U_{2}\) explains the gain in LUTs that the method proposed in this article gives. From the analysis of Table 10, it follows that for group G1, the following phenomenon takes place. In some cases, the circuits of FSMs \(U_{2}\) require fewer LUTs than it is for equivalent FSMs \(U_{3}\). This situation takes place for benchmarks: _bbara_, _dk15_, _ex2_, _ex7_, _keyb_, _s27_, and _s8_. However, for other benchmarks of G1, the circuits of FSMs \(U_{3}\) have better LUT counts than for equivalent FSMs \(U_{2}\). Let us explain this phenomenon. In LUT-based FSMs, the LUT counts depend on the relation among \(NA(\phi_{k})\) and \(I\). Both FSMs \(U_{2}\) and \(U_{3}\) include logic blocks generating outputs \(y_{n}\in Y\). Obviously, these blocks consume the same amount of LUTs. So, the difference in LUTs depends on LUT counts for other blocks of these FSMs. For FSMs \(U_{2}\), the number of LUTs depends on the distribution of FSM inputs among the functions belonging to SBFs (5), (9) and (10). For FSMs \(U_{3}\), the LUT count depends on relation among the value of \(2R_{Q}\) and the number of LUT inputs, I. If the condition (4) holds but the condition \(2R_{Q}\leq I\) is violated, then there are fewer LUTs in the circuits of FSMs \(U_{2}\) compared to the circuits of equivalent FSMs \(U_{3}\). We think that such situation takes place for the benchmarks _bbara_, _dk15_, _ex2_, _ex7_, _keyb_, _s27_, and _s8_. For other benchmarks of G1, the following situation takes place: the condition (4) is violated but the condition \(2R_{Q}\leq I\) holds. As a result, for these benchmarks, there are fewer LUTs in the circuits of FSMs \(U_{3}\) compared to the circuits of equivalent FSMs \(U_{2}\). It seems that this situation takes place for all benchmarks from the groups G2-G4. As a result, our approach allows obtaining better LUT counts for all benchmarks from these groups. As follows from Table 12, our approach produces slightly faster LUT-based FSM circuits compared to the three other investigated methods. The average win is equal to (1) 6.14% (compared with auto-based FSMs); (2) 6.9% (relative to one-hot-based FSMs); (3)1.42% (compared with \(U_{2}\)-based FSMs). The winning relative to \(U_{2}\)-based FSMs is especially important. It shows that our method not only improves the LUT counts, but also does not degrade the performance compared to three-block FSMs \(U_{2}\). Note that our approach loses in the performance of the obtained FSM circuits relative to JEDI-based FSMs (only 0.5%). For the group G0 (Table 13), our approach provides a gain relative to \(U_{2}\)-based FSMs (7.19%). However, other investigated methods win in the values of maximum operating frequency. The auto-based state encoding provides to 2.96% of gain. The JEDI-based state encoding provides 3.89% of gain. It means that our approach should not be applied if the number of LUT inputs is not less than the total number of FSM inputs (\(L\)) and state variables (\(R\)). So, for the group G0, there is the performance loss of SD-based FSMs in comparison with FD-based FSMs. This loss can be explained in the following way. Because the condition (4) holds, there is only a single logic level in the circuits of FD-based FSMs (auto, one-hot, JEDI). However, as follows from Figures 4 and 6, there are three logic levels in the circuits of \(U_{2}\)-based FSMs and two logic levels in the circuits of \(U_{3}\)-based FSMs. Therefore, the SD-based FSMs produce slower circuits compared to their FD-based counterparts. As follows from Table 14, for the group G1, our approach produces faster circuits than both auto- and one-hot-based FSMs. Our gain is equal to 3.92% and 4.04%, respectively. However, the FSM circuits produced by two other methods are slightly faster than \(U_{3}\)-based circuits. The JEDI-based FSMs win 2.9%. The \(U_{2}\)-based FSMs win 0.93%.