Bases and Number Representation

Numbers can be represented in various ways. For example, the number ‘four’ can be written in the usual notation as 4, in Roman numerals as IV, or even just as four tally marks, IIII. Similarly, ‘two-and-a-half’ can be written as the mixed number 2½, as the improper fraction 5/2, or as the decimal number 2.5. In particular, numbers can be represented using systems similar to the familiar decimal system but based on numbers other than 10. In this chapter, we investigate the representation of numbers using different number bases, paying particular attention to the number systems used in computing.