# High-Performance Digital Devices Design by the ASMD-FSMD Technique for Implementation in FPGA
## 4 Experiments and Discussion
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Example** & \(L_{T}\) & \(L_{A}\) & \(L_{T}\)/\(L_{A}\) & \(t_{T}\) & \(t_{A}\) & \(t_{T}\)/\(t_{A}\) \\ \hline mult\_c\_4 & 19 & 23 & 0.83 & 74.56 & 38.30 & 1.95 \\ mult\_c\_8 & 35 & 33 & 1.06 & 138.79 & 68.59 & 2.02 \\ mult\_c\_16 & 66 & 65 & 1.02 & 275.55 & 145.52 & 1.89 \\ mult\_c\_32 & 132 & 90 & 1.47 & 589.23 & 299.41 & 1.97 \\ mult\_c\_64 & 267 & 171 & 1.56 & 1241.75 & 629.66 & 1.97 \\ mult\_c\_128 & 528 & 462 & 1.14 & 2537.88 & 1239.05 & 2.05 \\ mult\_d\_4 & 20 & 13 & 1.54 & 89.49 & 37.54 & 2.38 \\ mult\_d\_8 & 36 & 24 & 1.50 & 157.24 & 69.26 & 2.27 \\ mult\_d\_16 & 65 & 41 & 1.59 & 305.59 & 145.28 & 2.10 \\ mult\_d\_32 & 124 & 90 & 1.38 & 619.21 & 307.82 & 2.01 \\ mult\_d\_64 & 267 & 170 & 1.57 & 1216.07 & 629.85 & 1.93 \\ mult\_d\_128 & 525 & 268 & 1.96 & 2466.98 & 1288.97 & 1.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The experimental results of the implementation of multipliers c and d by the Vivado tool. Figure 11: The comparison of \(L_{T}\)/\(L_{A}\) and \(t_{T}\)/\(t_{A}\) ratios for multipliers implemented by the Quartus tool. Additionally, a comparison of the maximum clock signal frequency was performed for all tested systems. The results are shown in Table 3, where \(F_{TC}\) and \(F_{AC}\) are the maximum frequency of clock in MHz in case of the traditional approach and when using the ASMD-FSMD technique for Cyclone 10 LP device and Quartus tool; \(F_{TK}\) and \(F_{AK}\) are the maximum frequency of clock in MHz in case of the traditional approach and when using the ASMD-FSMD technique for Kintex Ulftascale device and Vivado tool; \(F_{AC}/F_{TC}\) and \(F_{AK}/F_{TK}\) are relations of corresponding parameters. Table 3 shows that the maximum clock frequency for circuits described with the ASMD-FSMD technique in most cases was generally slightly higher than the maximum operation frequency of circuits developed with the traditional approach. It can also be seen that this frequency depends on the device and tool used. For the Cyclone device and Quartus tool, the advantage of the presented technique was higher than for the Kintex device and Vivado tool. This is the result of using different placing and routing algorithms in the design tools and differences in the architectures of the FPGA devices. Note that the Quartus and Vivado software tools were used with the default synthesis parameters. Thus, the effectiveness of the ASMD-FSMD technique does not depend on the  
Figure 12: The comparison of \(L_{T}\)/\(L_{A}\) and \(t_{T}\)/\(A_{A}\) ratios for multipliers implemented by the Vivado tool. \begin{table}
\begin{tabular}{l c c c c c c} \hline
**Example** & \(F_{TC}\) & \(F_{AC}\) & \(F_{AC}\)/\(F_{TC}\) & \(F_{TK}\) & \(F_{AK}\) & \(F_{AK}\)/\(F_{TK}\) \\ \hline mult\_c\_4 & 177.75 & 190.55 & 1.07 & 120.71 & 130.57 & 1.08 \\ mult\_c\_8 & 137.23 & 169.49 & 1.24 & 122.49 & 131.22 & 1.07 \\ mult\_c\_16 & 130.4 & 142.96 & 1.10 & 119.76 & 116.82 & 0.98 \\ mult\_c\_32 & 98.23 & 102.41 & 1.04 & 110.31 & 110.22 & 1.00 \\ mult\_c\_64 & 64.94 & 65.65 & 1.01 & 103.89 & 103.23 & 0.99 \\ mult\_c\_128 & 36.99 & 39.31 & 1.06 & 101.27 & 104.11 & 1.03 \\ mult\_d\_4 & 194.78 & 209.38 & 1.07 & 122.93 & 133.19 & 1.08 \\ mult\_d\_8 & 181.88 & 192.09 & 1.06 & 120.83 & 129.94 & 1.08 \\ mult\_d\_16 & 156.99 & 197.94 & 1.26 & 114.53 & 117.01 & 1.02 \\ mult\_d\_32 & 135.21 & 153.09 & 1.13 & 108.20 & 107.20 & 0.99 \\ mult\_d\_64 & 97.05 & 125.6 & 1.29 & 107.72 & 103.20 & 0.96 \\ mult\_d\_128 & 62.33 & 79.95 & 1.28 & 104.99 & 100.08 & 0.95 \\ \hline \end{tabular}
\end{table} 
Table 3: Maximum operating frequency of the implemented multipliers. design tool used (Quartus or Vivado), and the effectiveness of the ASMD-FSMD technique is determined solely by describing the behavior of the digital device in the ASMD chart. The improved performance of digital devices is due to the efficient implementation of Verilog compilers.