(untitled) (Global Journals of Research in Engineering, 2022)
An alternate method of representation of number system is proposed. The alternate method is based on reflection (0) and inverted reflection (1). Using an inverted reflected plane, one can create consecutive places of a number system. The alternate method has the advantage of creating empowered system representation with all places of the same power of the base. Three axioms are identified and can be proved by the method of mathematical induction to complete the process. The three axioms are, a creation of number system using inverted reflection, unique non-repetitive inverted reflection count generates natural numbers and taking inverted reflection with sign bit generates two’s complement representation of negative numbers. It enabled us to create any desired number system and explained with the help of two versions of the decimal system. Typically, powered system representation leads to random switching within the representation. Contrary to that, new representation provides uniform switching and minimal uniform switching thus minimising glitch. Through this method, one proves that thermometer coding act as a number system so that all arithmetic operations are possible with thermometer coding. New representation brings out the fact that decimal representation confirms to dual form, in binary form is empowered representation and in decimal digit form powered representation. Uniform switching representation of decimal digit resembles the human finger digit, and its dual representation leads to exploiting symmetry.