AbstractThe traditional neural system which conducts the paired association has the real coupling coefficients and is not suited to the implementation on digital processing LSI because of its analog property.From such a viewpoint, this paper applies the traditional idea of calculating the coupling coefficients on the real field to the binary field and proposes a system which conducts the paired association using only the logic operation. More precisely, it is noted that the associative law applies to the matrix operation on the real field as well as the matrix operation for the binary code.The coupling coefficients for the binary code for the paired association are derived by applying the sweeping‐out method to the matrix of binary numbers. By this approach, a paired‐associate system is obtained by a simpler training algorithm with easy LSI implementation.This paper describes first the traditional solution of the paired‐associate problem on the real field and then proposes a method of solution based on that approach for the paired‐associate problem on the binary field. The existence condition for the solution of the paired‐associate problem is discussed for the proposed method. Finally, the noise‐reduction power of the proposed method i