The ability to estimate and produce appropriately timed responses is central to many behaviors including speaking, dancing, and playing a musical instrument. A classical framework for estimating or producing a time interval is the pacemaker-accumulator model in which pulses of a pacemaker are counted and compared to a stored representation. However, the neural mechanisms for how these pulses are counted remain largely unaddressed. We present a biophysical model of how to keep count of cycles of a pacemaker clock. Our model utilizes a system of bistable Wilson-Cowan units asymmetrically connected in a one-dimensional array; all units receive the same input pulses from a central clock but only one unit is active at any point in time. With each pulse from the clock, the position of the activated unit changes thereby encoding the total number of pulses emitted. This neural architecture maps the counting problem into the spatial domain, which in turn translates count to a time estimate thus allowing the mechanism to be used in time interval production and estimation. The encoding of count using discrete states allows our mechanism to overcome sensitivity to two sources of noise: noise internal to the neural units themselves and variability that arises from using a stochastic oscillator as the pacemaker. Furthermore, this discrete representation overcomes the need for the fine-tuning of parameters that is a known criticism of the linear integrator model. Lastly, we extend the model to a hierarchical structure to be able to robustly achieve higher counts using fewer units.