## 3 Results
### Packet Assembling and Sending Times
Below, we present more detailed results for the decimal number representation (D) and the hexadecimal number representation with bit-shift (HS), which is the better-performing of the two hexadecimal versions. To maintain readability, we have not included all measurement results in the manuscript. However, the complete dataset is available upon request. Table 3 shows the mean packet assembly time with its standard deviation (it can be observed that the standard deviation of our results is small, in the range of a few percent of the mean values. It occurs for two main reasons: (a) differences in central frequencies of low-quality oscillator of the microcontroller boards, (b) inaccuracies of manual reading of oscilloscope measurement results) and Table 4 shows the mean packet send times with its standard deviation for different sensor sampling frequencies and different numbers of samples per packet using the decimal number representation. Although this format is less efficient than the hexadecimal alternative, it is very useful for rapid prototyping and low-demand wearable sensor systems--particularly in scenarios when low sampling frequencies are sufficient. Our measurements show that, using the decimal format, it is possible to send up to 10 sensor samples per packet, with maximum achievable sampling frequencies of 450 Hz, 550 Hz, and 650 Hz for 1, 2, and 5/10 samples per packet, respectively. In high-demand wearable sensor systems, we have to use the hexadecimal representation. Figures 8 and 9 present a comparative analysis of mean packet assembly and transmission times when using an optimized hexadecimal representation with bit-shifting techniques. We do not show the results of the standard deviation as they are in the range of a few percent of the mean values and would not stand out in the graph. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & \multicolumn{2}{c}{**Assembly Time [ms]**} & \multicolumn{2}{c}{**Send Time [ms]**} \\ \hline
**Format** & **Max f\({}_{\text{s}}\) [Hz]** & **Mean** & **STD** & **Mean** & **STD** \\ \hline
1D & 450 & 0.458 & 0.002 & 1.360 & 0.001 \\
2D & 550 & 0.918 & 0.008 & 2.253 & 0.013 \\
5D & 650 & 2.640 & 0.014 & 4.435 & 0.050 \\
10D & 650 & 5.625 & 0.026 & 8.550 & 0.075 \\ \hline
1H & 600 & 0.127 & 0.001 & 1.124 & 0.002 \\
5H & 1150 & 0.953 & 0.008 & 2.935 & 0.005 \\
10H & 1300 & 1.890 & 0.020 & 5.430 & 0.010 \\
26H & 1300 & 5.500 & 0.042 & 14.080 & 0.031 \\ \hline
1 HS & 650 & 0.040 & 0.005 & 1.107 & 0.009 \\
5 HS & 1350 & 0.195 & 0.005 & 3.100 & 0.005 \\
10 HS & 1550 & 0.713 & 0.002 & 5.211 & 0.001 \\
26 HS & 1750 & 2.300 & 0.007 & 12.060 & 0.035 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Maximal achieved sampling frequency, mean times with their standard deviation for assembling, and sending packets at different number of samples in one packet in three different formats. A number in row represents the number of samples and letters the ASCII format used to represent values: D = decimal, H = hexadecimal, HS = hexadecimal calculated by a bit-shift operation. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Mean Send Time [ms]**} & \multicolumn{6}{c}{**STD of Send Time [ms]**} \\ \hline \(f_{\text{s}}\) **[Hz]** & **1D** & **2D** & **5D** & **10D** & **1D** & **2D** & **5D** & **10D** \\ \hline
100 & 0.446 & 0.905 & 2.270 & 4.525 & 0.001 & 0.004 & 0.010 & 0.009 \\
200 & 0.452 & 0.901 & 2.260 & 4.515 & 0.002 & 0.002 & 0.022 & 0.009 \\
450 & 0.458 & & & & 0.001 & & & \\
500 & N/A & 0.899 & 2.623 & 5.220 & N/A & 0.008 & 0.043 & 0.010 \\
550 & 0.918 & & & & 0.013 & & & \\
600 & N/A & 2.603 & 5.555 & & N/A & 0.045 & 0.058 \\
650 & & N/A & 2.640 & 5.625 & & N/A & 0.050 & 0.075 \\
700 & & N/A & N/A & N/A & N/A & N/A & N/A \\ \hline \end{tabular}
\end{table} 
Table 4: Mean packet send times with their standard deviation for different sensor sampling frequencies \(f_{\text{s}}\) and different number of samples in one packet for the decimal format. A number in column labels represents the number of samples per packet.