A digital synthesizer (18) includes a memory (12) containing values representing amplitudes of a signal such as a sinewave, a digital/analog converter (14) for converting outputs from the memory into an analog signal, and a counter (10) for counting by a predetermined fixed increment, which operates at a high frequency to enable the generation of very precise frequency waveforms. The digital synthesizer has many practical applications including the generation of precise signals to extract information from input radio frequency signals, the obtaining of a precise frequency from a low-cost clock, and the use as a component of a FSK modulator to permit selection between signals of multiple frequencies without any phase discontinuity. Finally, the digital synthesizer can be used in combination with an 8-bit memory, to generate a 10-bit input to a digital-to-analog converter.