As the ability to perform computation increased from the early days of computers and up to the present so was the knowledge how to utilize the hardware and software to perform computation.Digital computer arithmetic emerged from that period in two ways: one as an aspect of logic design and other as development of efficient algorithms to utilize the available hardware. Given that numbers in a digital computer are represented as a string of zeroes and ones and that hardware can perform only relatively simple and primitive set of Boolean operations, all of the arithmetic operations performed are based on a hierarchy of operations that are built upon the very simple ones.

What distinguishes computer arithmetic is its intrinsic relation to technology and the ways things are designed and implemented in a digital computer. This comes from the fact that the value of a particular way to compute, or a particular algorithm, is directly evaluated from the actual speed with which this computation is performed. Therefore there is a very direct and strong relationship between the technology in which digital logic is implemented to compute and the way the compu-tation is structured. This relationship is one of the guiding principles in development of the com-puter arithmetic.