Several new concepts, such as pseudoprime and modulo correlativity, are presented. Then modulo subtraction and modulo division, which are very useful in computing the canonical expansion, are proposed in a multiple valued modulo algebra system with either a prime or a composite radix. Finally the completeness of modulo operations and the current mode CMOS circuit design for any unary function are discussed on the basis of modulo correlativity. This method is also applicable to a high-radix multiple valued modulo algebra system.
The paper presents the concepts of pseudoprime and modulo correlativity and establishes the relationships among completeness of modulo operations, uniqueness of solution of equations, invertibility of a square matrix, and correlativity of vectors in multiple-valued modulo system. It is shown that current-mode CMOS circuits are easy to design and economical using bounded operations. I
For the deficiencies of the existing complex circuit designs, a novel transistor-level three-input AND/XOR logic complex gate with simple and symmetry structure is proposed. HPSICE simulation results show that the proposed circuit has correct operation. Further, in 55nm process CMOS technology, compared with the conventional cell-based cascaded AND/XOR circuit at different operation frequencies, the proposed circuit has a significant improvement at delay, power consumption and power delay product (PDP).
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