On the Conversion Between Number Systems

This brief revisits the problem of conversion between number systems and asks the following question: given a nonnegative decimal number d, what is the value of the digit at position j in the corresponding base b number? Thus, we do not require the knowledge of other digits except the one we are interested in. Accordingly, we present a conversion function that relates each digit in a base b system to the decimal value that is equal to the base b number in question. We also show some applications of this new algorithm in the areas of parallel computing and cryptography