## 4 Modified Method Based on MRC
The outputs of the multipliers are connected to the inputs of \(n\) modular adders modulo \(p_{i}\), \(i=\overline{1,n}\), and the output of the multiplier by \(\hat{b}_{1,1}\) is connected to the input of the first modular adder modulo \(p_{1}\) and performs calculations \(\hat{x}_{1}=\left|U_{1}\right|_{p_{1}}=\left|x_{1}\cdot\hat{b}_{1,1}\right|_{ p_{1}}\), \(\sigma_{1}=\left|\frac{x_{1}\cdot\hat{b}_{1,1}}{p_{1}}\right|\), the value \(\hat{x}_{1}\) goes to the output of the first modular adder modulo \(p_{1}\), the value \(\sigma_{1}\) goes to the carry output of the first modular added modulo \(p_{1}\). The outputs of the multipliers by \(\hat{b}_{1,2}\) and by \(\hat{b}_{2,2}\) are connected to the inputs of the second modular adder modulo \(p_{2}\), whose carry input is connected to the carry output of the first modular adder modulo \(p_{1}\), and calculates \(\hat{x}_{2}=\left|\sigma_{1}+U_{2}\right|_{p_{2}}=\left|\sigma_{1}+x_{1}\cdot \hat{b}_{1,2}+x_{2}\cdot\hat{b}_{2,2}\right|_{p_{2}}\), \(\sigma_{2}=\left|\frac{\sigma_{1}+x_{1}\cdot\hat{b}_{1,2}+x_{2}\cdot\hat{b}_{ 2,2}}{p_{2}}\right|\), the value of \(\hat{x}_{2}\) goes to the output of the second modular adder  
\[P_{2}=7\cdot 9=63,\quad\left|P_{2}^{-1}\right|_{p_{2}}=\left|63^{-1} \right|_{8}=7,\quad B_{2}=441,\]5 Computational unit for translating numbers from RNS and expanding bases. modulo \(p_{2}\), the value of \(\sigma_{2}\) goes to the carry output of the second modular adder modulo \(p_{2}\). Therefore, the outputs of the multipliers by \(\hat{b}_{i,n}\), \(i=\overline{1,n}\), are connected to the inputs of the \(n-th\) modular adder modulo \(p_{n}\), whose carry input is connected to the carry output of the \((n-1)\)-th modular adder modulo \(p_{n-1}\), and calculates \(\hat{x}_{n}=\left|\sigma_{n-1}+U_{n}\right|_{p_{n}}=\left|\sigma_{n-1}+\sum_{i =1}^{n}x_{i}\hat{b}_{i,n}\right|_{p_{n}}\), \(\sigma_{n}=\left|\frac{\sigma_{n-1}+\overline{1,n}\times x_{i}\hat{b}_{i,n}}{p _{n}}\right|\), the value \(\hat{x}_{n}\) arrives at the output \(n\) of the modular adder modulo \(p_{n}\), the value of \(\sigma_{n}\) arrives at the carry output of the \(n-\)th modular adder modulo \(p_{n}\), which is not connected to other elements. The values of \(\hat{x}_{i}\) from the outputs of \(i\)-th modular adders modulo \(p_{i}\) are fed to the inputs of \(i\)-th multipliers by the bases of MRC \(\hat{w}_{i}\), \(i=\overline{1,n}\), where multiplication of \(\hat{x}_{i}\) by \(\hat{w}_{i}=\prod_{j=1}^{i-1}p_{j}\) takes place. The output of the \(i\)-th multiplier by the bases of the MRC \(\hat{w}_{i}\) is connected to the \(i\)-th inputs of the adder and the modular adder, \(i=\overline{1,n}\), the input of the extended base of the modular adder receives the modulo value \(p_{n+1}\), the output of the reduced number of the adder receives the reduced number \(X\) in the positional number system, and the output of the remainder on the extended basis of the modular adder receives the number on the extended basis, i.e., \(\left|X\right|_{p_{n+1}}\). This method has a similar matrix structure to New CRT, but uses a sequential calculation without the remainder over a large modulo, as in MRC.