Spin half-adder in $\mathcal{B}_{3}$

Spin half-adder in $\mathcal{B}_{3}$

This study is about spin half add operations in $\mathcal{B}_{2}$ and $\mathcal{B}_{3}$. The burden of technological structures has increased due to the increase in the use of today"s technological applications or the processes in the digital systems used. This has increased the importance of fast transactions and storage areas. For this, less transactions, more gain and storage space are foreseen. We have handle tit (triple digit) system instead of bit (binary digit). $729$ is reached in $3^{6}$ in $\mathcal{B}_{3}$ while $256$ is reached with $2^{8}$ in $B_{2}$. The volume and number of transactions are shortened in $\mathcal{B}_{3}$. The limited storage space at the maximum level is storaged. The logic connectors and the complement of an element in $\mathcal{B}_{2}$ and the course of the connectors and the complements of the elements in $B_{3}$ are examined. "Carry" calculations in calculating addition and "borrow" in calculating difference are given in $\mathcal{B}_{3}$. The logic structure $\mathcal{B}_{2}$ is seen to embedded in the logic structure $\mathcal{B}_{3}$. This situation enriches the logic structure. Some theorems and lemmas and properties in logic structure $\mathcal{B}_{2}$ are extended to logic structure $\mathcal{B}_{3}$.

This study is about spin half add operations in $\mathcal{B}_{2}$ and $\mathcal{B}_{3}$. The burden of technological structures has increased due to the increase in the use of today"s technological applications or the processes in the digital systems used. This has increased the importance of fast transactions and storage areas. For this, less transactions, more gain and storage space are foreseen. We have handle tit (triple digit) system instead of bit (binary digit). $729$ is reached in $3^{6}$ in $\mathcal{B}_{3}$ while $256$ is reached with $2^{8}$ in $B_{2}$. The volume and number of transactions are shortened in $\mathcal{B}_{3}$. The limited storage space at the maximum level is storaged. The logic connectors and the complement of an element in $\mathcal{B}_{2}$ and the course of the connectors and the complements of the elements in $B_{3}$ are examined. "Carry" calculations in calculating addition and "borrow" in calculating difference are given in $\mathcal{B}_{3}$. The logic structure $\mathcal{B}_{2}$ is seen to embedded in the logic structure $\mathcal{B}_{3}$. This situation enriches the logic structure. Some theorems and lemmas and properties in logic structure $\mathcal{B}_{2}$ are extended to logic structure $\mathcal{B}_{3}$.