Today's PCs can directly manipulate numbers not longer than 64 bits because the size of the CPU registers and the data-path are limited. Consequently, arithmetic operations such as addition, can only be performed on numbers of that length. To solve the problem of computation on big-integer numbers, different algorithms were developed. However, these algorithms are considerably slow because they operate on individual bits; and are only designed to run over single-processor computers. In this paper, two algorithms for handling arithmetic addition on big-integer numbers are presented. The first algorithm is sequential while the second is parallel. Both algorithms, unlike existing ones, perform addition on blocks or tokens of 60 bits (18 digits), and thus boosting the execution time by a factor of 60.