Numbers And The Machine

EE 50 December 1987 NUMBERS AND THE MACHINE by C.H. Freeman Computer science depends largely on the properties of real numbers. The correct use of these requires an understanding of the mathematic basis of the real number system. Unfortunately, many people shy away from anything mathematical, even if it has only to do with numbers. This article attempts to allay these misgivings. Modern man counts in base ten, that is, he uses the ten in- dividual symbols 0, 1, 2,...,8, 9. Obvious, you might say, but it hasn"t always been so. Some races have been known to count in base 20 (by using their toes and fingers in arithmetical operations) and the concept of zero itself is quite new; conse- quently, the Romans, who had no representation for zero, had endless trouble with arithmetic. In general, an n digit integer, No, can be represented by No = dnRn do-1R n-1 +diR1 + doRo or No = E diRr r=° where d", d2, decimal symbols in the coun- ting system and R is the number base we are working in....