Multiwave optical computing, where discrete wavelengths are employed as multiplexable information carriers, presents an interesting solution to the communication crisis in next-generation integrated systems. A computer architecture using multiwavelength opto-electronic integrated circuits (multiwave OEICs) provides the wavelength space as extra dimension of freedom for parallel processing. A key feature is that several independent computations can be performed in a single optical circuit using wavelength space, as if it were several computing circuits operating in parallel. The model of basic logic gates for multiwave (four-wave) computing circuits is shown. The functions, union, complement, and wavelength conversion, form a functionally-complete set of logic operations for constructing arbitrary multiwave computing circuitry. An experimental system demonstrating the concept of multiwave computing as well as wavelength-space routing is shown. This architecture will have wide range of applications in parallel processing systems for which interconnection is a major issue. In this level of organization, embedding complicated global communication topology into wavelength space provides significant advantages. In a class of parallel processing architectures based on bit-permute-complement (BPC) connections (e.g., perfect-shuffle network, FFT network, Batcher's sorting network, etc.), two-dimensional reduction of interconnection area by the factor of 1/r2 is expected with r wavelength components.