Optics has already proved its strong potentiality for the conduction of parallel logic, arithmetic and algebraic operations. In the last few decades several all-optical data processors were proposed. To implement these processors different data encoding/decoding techniques have been reported. In this context, polarization encoding technique, intensity-based encoding technique, tristate and quaternary logic operation, multivalued logic operations, symbolic substitution techniques etc. may be mentioned. Very recently, frequency encoding/decoding technique has drawn interest from the scientific community. Frequency is the fundamental character of any signal; and it remains unaltered in reflection, refraction, absorption etc. during the propagation and transmission of the signal. This is the most important advantage of frequency encoding technique over the conventional encoding techniques. In this communication the authors propose a new scheme for implementing NOT, OR and NOR logic operations. For this purpose co-propagating beams having different frequencies in C-band (1535–1560 nm) have been used for generating cascaded sum and difference frequency, exploiting the nonlinear response character of periodically poled LiNbO3 waveguide. The cross-gain modulation property of the semiconductor optical amplifier (SOA) and the wavelength conversion property of the reflecting semiconductor optical amplifiers (RSOA) are exploited here to implement the desired optical logic and arithmetic operations.