The objective of this work is to analyze pulsed digital oscillators (PDOs), as dynamical systems. It is proved that under some conditions, the bitstream at the output of the oscillator is that of the sign of a sampled sinusoid at the resonant frequency of the resonator, and that a bijection exists between these sequences (without distinguishing between a sequence and its negated version) and those of first-order sigma-delta modulators. This provides a new and simple method of obtaining the oscillation frequency of PDOs just from their bitstream.