An arithmetic formula is discovered that can be used to reduce logic to arithmetic. The formula enables a logic algorithm to be reduced to an arithmetic algorithm without the use of logical trees, thereby converting a logical operation to an arithmetic operation. The use of the arithmetic formula enables the computation of functions that use Boolean logic. The operation of a computer program relies on logic circuits, which in turn implement Boolean logic. Considering that a computer program requires a minimum of one or more logic circuits to execute, it now becomes possible to replace the functions of these logic circuits by a computer program implementing the arithmetic formula. Therefore, it is possible to develop software that functions similar to a real processor.