1/101 is then added, the result is 10001/999900. The size of arbitrary-precision numbers is limited in practice by the total storage available, the variables used to index the digit strings, and computation time. A 32-bit operating system may limit available storage to less than 4 GB. A programming language using 32-bit integers can only index 4 GB. If multiplication is done with a Θ {\displaystyle \Theta } (N2) algorithm, it would take on the order of 1012 steps to multiply two one-million-word numbers. Numerous algorithms have been developed to efficiently perform arithmetic operations on numbers stored with arbitrary precision. In particular, supposing that N digits are employed, algorithms have been designed to minimize the asymptotic complexi