Computer Progress in Czechoslovakia
Antonı́n Svoboda · 1962
Before the era of the high-speed electronic digital computers the representation of numbers in the decimal numerical form was exclusively used in computational practice. The design of the first program-controlled mathematical machines (for instance, Harvard Mark I and ENIAC) was also based on the decimal number system. It took long time before the merit of other polyadic form (for instance, the dyadic or binary number system) was recognized for this purpose. Compatibility with the switching properties of electronic elements and simplicity of logic are outstanding features claimed for the use of the binary system. The algorithms for the arithmetic operations in computing machines can also be based on a numerical system which is not polyadic, i. e. on the numerical System of Residual Classes (SRC). The SRC-encoding of numbers in computers has certain unexpected theoretical as well as practical features. To begin with, the theoretical background of SRC number representation and characteristics of SRC arithmetic operations and algorithms are presented in this paper in form of a condensed survey appended by some elucidating examples. The question of encoding of numbers to be transmitted through the data channels and processed in the SRC arithmetic unit is considered to be of predominant importance as to its practical applicability. There are two basic methods of encoding which are known and which have already been used at advantage to design computing circuits: the one-out-of-n code to represent n integers by n bits and the combinatory code of representing 2 n integers by n bits. The SRC permits to develop another system of encoding which is, in fact, a combination of the two methods of encoding mentioned above. Logical circuits for arithmetic operations based on this type of coding have certain interesting features which are discussed in the paper. The author is aware of the fact that his effort to present a clear and unified picture of the SRC is certainly far from being satisfactory. The SRC is only, in its first stages of evolution, influenced by practical applications in computing machines. New conceptions, algorithms and logical circuits can be expected for the future.