The subject invention pertains to a method and apparatus for performing computations using residue arithmetic. The subject method and apparatus can utilize logic gates for performing calculations such as multiplication by a constant, computing a number theoretic logarithm of a residue for a given base αi and modulus pi and computing the product of two residues, modulo Pi- The use of logic gates can offer advantages when compared with the use of ROMs for table look-up functions in integrated RNS digital signal processor implementations.