The concept of a mixed-radix multiple-valued input exclusive sum of products (MRESP) is presented, and some possible circuit realizations for the concept are discussed. The algorithm starts from a Boolean function and generates an approximate MRESP form and the appropriate multioutput circuit. Such circuits can have smaller complexity than the EXOR forms with mixed polarity, the PLAs with decoders, and the networks with two-variable function generators. They are also easily testable. >