Codes

Abstract

Practically no electronic computers have been designed with a different arithmetic system than that based on the number system with radix 2, the binary system. Some computers operate with numbers in the binary system, others with numbers in the decimal system, however, the decimal digits are then represented in the binary number system. Although this book does not intend to give a survey of different number systems used in history for calculation, a couple of historic facts about the binary system should be mentioned. The binary number system is not an invention specially made for the design of the first electronic computers. Its invention as a number system may be attributed to the Chinese emperor-philosopher Fohy (± 2000 b.c.). We owe our knowledge that the binary number system is suitable for the arithmetic operations addition, subtraction, multiplication and division to G. W. Leibniz (1703), who wrote the first treatise on the subject Explication de l’Aritmétique Binaire (Boudot, Paris) after thinking for more than 20 years about the ‘dyadica’ or binary arithmetic1. Basically nothing has changed since then.