A family of all essential Radix-2 addition/subtraction multi-polarity transforms: algorithms and interpretations in Boolean domain

By investigating some families of elementary order-2 matrices, new transforms of real vectors are introduced. When used for Boolean function transformations these transforms are one-to-one mappings in a binary/ternary vector space. The concept of different polarities of considered arithmetic and adding transforms is introduced. The links of arithmetic and adding transforms with classical logic design are discussed