The prototype quantum random number (random bit) generators (QRNG) consists of one photon at a time falling on a $50:50$ beam splitter followed by random detection in one or the other other output beams due to the irreducible probabilistic nature of quantum mechanics. Due to the difficulties in producing single photons on demand, in practice, pulses of weak coherent (laser) light are used. In this paper we take a different approach, one that uses moderate coherent light. It is shown that a QRNG can be implemented by performing photon-number parity measurements. For moderate coherent light, the probabilities for obtaining even or odd parity in photon counts are $0.5$ each. Photon counting with single-photon resolution can be performed through use of a cascade of beam splitters and single-photon detectors as was done recently in a photon-number parity-based interferometry experiment involving coherent light.
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