This work explores randomness enhancing capability of asynchronous cellular automata. This paper first reports theoretical results to identify elementary cellular automata under fully asynchronous updating scheme with large cycle of length 2(n) or 2(n) - 1. To predict the randomness enhancing capability, we classify these large cycle asynchronous cellular automata into fully and partially exposed systems following both the experimental and theoretical approach. Finally, it is observed that fully exposed asynchronous cellular automata are able to improve randomness quality of a 'poor' random number generator.