This paper deals with new results that benefit the transformation, process and the conversion from a numerical system to another without using the previously well-known rules like progressive division on the system basis or through the number expansion according to the new system basis [6]. In our work, we depend on a new pattern in the transformation process according to well-known numbers [2] and [4] used in computing systems in the forms      and linear transformation and algebraic complement.

numerical systems, decimal systems, binary system, octal systems, hexadecimal systems.