Error control by product codes in arithmetic units

Product (AN) codes constructed in weighted number systems are investigated with the aim of devising error control features suitable for application in arithmetic units. The previous theoretical framework, which was derived in the hypothesis of codes defined in a virtual range M = k A, is restated for any physical interval M = bn, where b is the radix of the system and n is the number of digits. Some general properties holding for radix-b-AN codes are reconsidered and necessary and sufficient conditions for single and double error detection are derived for binary codes and for a sample non binary case. Single error correction is discussed as well and a fast error decoding procedure is suggested and implemented. Finally, modular AN codes are introduced in order to enable the use of product codes in standard ALU's representing relative integers by means of a radix complement notation. It is shown that the above properties keep their validity and that concurrent single error correction can be associated with arithmetic computation without increasing the time spent for processing.