A communications device includes at least one memory device for storing complex exponential functions as approximations of sine and cosine basis waveforms. A logic circuit adds and subtracts the complex exponential functions to generate an Orthogonal Frequency Division Multiplexed (OFDM) communications signal as a plurality of N data subcarriers that carry communications data. The logic circuit provides efficient and accurate implementation of the IFFT for use as an OFDM modulator using additions of stored complex exponentials and modulation of the integer-valued QAM data symbols using logic shifts and sign changes (2's complement).