Performing Arithmetic
So far, we have looked at how binary numbers can be used to represent a variety of data and they can be manipulated to form new numbers such as in the case of performing addition on them. But what about subtraction and the remaining arthmetic oprerations, multiplication and division?
We should note that the basic design of computers are such that generally the ability to perform addition as a primitive operation of the CPU is hard-wired into the circuitry. Fortunately too, using positional numbers and properties of algebra, it turns out that if a machine can perform addition, it can in principle perform all four arithmetic operations so long as appropriate instructions for interpreting the sequences of bits can be implemented into the system; this is one of the primary roles of software.
Without dwelling on the low-level technical aspects, we can at least get a glimps of how binary numbers alone can be used to perform other arthmetic operations.