This is a unique representation up to the maximum number expressible by the basis (here 2 * 3 * 5 = 30). Both addition and multiplication can be expressed as simple algorithms, but if turns out to be difficult to compare numbers. However, a good deal of investigation has gone into residue arithmetic as a possible alternative internal representation of numbers.

For RTM's none of the above representations seem to be an alternative to the binary representation. Our example of multiplication was ill conceived to illustrate gains to be made by changing representation. If we had chosen the example of checkers (recall the two representations in Chapter 1), the story would have been quite different. Here the basic hardware system is not already specialized to the representation of checkerboards (as it is to numbers). Each different internal representation of the board has distinctly different and non-

134