The paper is concerned with analyzing the effect of finite wordlength on the tracking performance of a signed regressor algorithm when used in the adaptive identification of a time-varying plant. Rounding quantization is assumed. Expressions of the steady state mean square error, steady state mean square weight deviation, and the corresponding optimum step sizes are derived. It is found that the mean square error, mean square weight deviation, and the optimum step sizes increase as the filter weight wordlength decreases. The effect of filter weight wordlength is found to be equivalent to an increase of the degree of nonstationarity and/or the noise of the plant. It is also found that the effect of filter weight quantization dominates the effect of input quantization. The theoretical results of the paper are validated by computer simulations.