A common method for generating truly random numbers is to generate pulses in a Poisson process, and count these modulo N. It is well known that, for a large counting interval, the digit held by the counter at the end of the interval is a random digit in the interval (O, N-1). In practice, however, 'dead time' in the counter prevents all the pulses from being counted. The effect of this is that those pulses which are actually counted arrive, not in a Poisson process, but in a renewal process. The main conclusion of this paper is that the resulting count modulo N remains uniformly distributed on (0, N-1) under this more general assumption.