Sine-wave synthesizers are a core requirement in many electronic applications, such as communication systems, and test and verification of analog/mixed-signal electronic systems. In sine-wave synthesizers, there exists a compromise between output spectral purity and hardware complexity. Harmonic-cancelling sine-wave synthesizers (HCSSs) allow spectrally pure signal synthesis at low hardware cost, compared to conventional sine-wave synthesis approaches. In this paper, we propose a digital HCSS hardware architecture, which is simpler, more hardware efficient and more programmable compared to state of the art HCSSs. The proposed architecture has been verified through a prototype built from an FPGA and discrete components. Prototype results demonstrate 51.9 dBc spurious free dynamic range (SFDR) and an output frequency range from 100 Hz to 100 kHz.