Implementation of Finite State Automata (FSA) Chart in the Process of Calculation of the Remainder of Two Numbers with an Infinite Many Digits

Electronic devices similar to calculator, both physical and application, are equipped with a feature to calculate the remainder (read: modulo) of two independent numbers. The problem is that there is a limited size of the display screen and memory to accommodate data on the device so that the number of digits to be processed is very limited. This research offers a solution in the form of using a Finite State Automata (FSA) chart to carry out the process ofcalculating the remainder of two independent numbers A and B with an unlimited number of digits, where A is the numerator and B is the denominator, written in the format A mod B. Second A and B values must be integers. The value of numerator must be greater than the denominator so that the process of calculating the remainder can be carried out, because if the value of the numerator is the same as the denominator then the remainder is 0 (zero), whereas if the value of the numerator is less than the denominator then the remainder is the same as the numerator itself. The remainder of the quotient is a number between 0..(B-1). The use of FSA chart in this research will ensure that the calculation process will take place in stages for each digit of the numerator being processed. This method also allows the process to be stopped at any time to see the remainder of the results from the starting digit to the digit at the stopping point. From the experiments that have been carried out, we obtained perfect accuracy results from the FSA chart when used to calculate the remainder for any value A and B even though the number of A digits is very large. Thus, this research can be an alternative method for calculating the remainder of two independent numbers.