## 4 Performance Analysis of Basic SC Unit  
### Computational Accuracy of Basic SC Unit  
To ascertain the computational performance of the algorithm proposed in this paper, an initial analysis was conducted regarding the computational accuracy of the basic SC units. A total of 10,000 sets of random sequences, uniformly distributed within the range of \(-1\) to 1, were employed as input data in order to minimize the statistical errors. The outcomes derived from floating-point computations served as the benchmark values, and the Root Mean Square Error (RMSE) was utilized to quantify and evaluate the computational performance of the various computing units. Figure 9: Multi-stream design for the MSD algorithm. Figure 10 illustrates the computational accuracy of the stochastic inverter. As the inverter has only a single input and its circuit does not introduce inherent computational errors, the errors associated with the inverter stem only from the data conversion process of the SNG. As the sequence length increases, the statistical error can be reduced, leading to an enhancement in the computational accuracy of the inverter. Distinct from the inverter, the computational results of the multiplier can be influenced by the correlation between the two input sequences. In this study, we introduced the SC correlation (SCC) methodology, as outlined in reference [30], and the corresponding calculation equation can be expressed as  
\[SCC(X,Y)=\left\{ \begin{array}{ll}\frac{ad-bc}{n\times\min(a+b,a+c)-(a+b)(a+c) }&ifad>bc\\ \frac{ad-bc}{(a+b)(a+c)-n\times\max(a-d,0)}&otherwise\end{array} \right. \tag{29}\]  
where \(a\) is the number of overlapping 1s in X and Y, \(b\) is the number of overlapping 1s in X and 0s in Y, \(c\) is the number of overlapping 0s in X and 1s in Y, and \(d\) is the number of overlapping 0s in X and Y. When the SCC is +1, it signifies maximum similarity between the two sequences. Conversely, when the SCC is \(-1\), it indicates the minimum similarity (maximum difference) between the sequence and, when the SCC is 0, it implies that the two sequences are independent. Figure 11 illustrates the computational accuracy of the multiplier with input sequences exhibiting different correlation levels. When the two input sequences are independent, the computational accuracy of the multiplier progressively enhances as the sequence length increases. Under such conditions, the computational error of the multiplier primarily arises from errors during the numerical domain conversion of the two random sequences. When a notable degree of correlation is present between the two input sequences, the computational error becomes more pronounced. This error mainly stems from the deviations in the computation results due to the sequence correlation. As a result, even with an increase in the sequence length, there is generally no discernible enhancement in the computational accuracy. Figure 10: The RMSE of the inverter unit. Figure 12 compares the performance of the proposed adders with those presented in references [36; 37; 38; 39; 40]. When N = 2 and k = 1, the adder proposed in this study, similar to the one presented in reference [40], is a non-scaled adder. The experimental results indicate that the computational error of the proposed adder is basically equivalent to that of reference [40]. Therefore, the proposed adder will not introduce additional computational errors. The adders described in Reference [37] and Reference [39], which also incorporate distinct methodologies to mitigate computational errors during their calculation procedures, are scaled adders with a scaling factor of one half. The computational error of the proposed adder is slightly higher than that of the adders in Reference [37] and Reference [39]. Figure 13 illustrates the computational accuracy under diverse configurations of the proposed adder with different reference sequences.