Sleep deprivation adversely affects the ability to perform cognitive tasks, but theories range from predicting an overall decline in cognitive functioning (because of reduced stability in attentional networks) to claiming specific deficits in executive functions. In the present study, we measured the effects of sleep deprivation on a two-choice numerosity discrimination task. A diffusion model was used to decompose accuracy and response time distributions in order to produce estimates of distinct components of cognitive processing. The model assumes that, over time, noisy evidence from the task stimulus is accumulated to one of two decision criteria and that parameters governing this process can be extracted and interpreted in terms of distinct cognitive processes. The results showed that sleep deprivation affects multiple components of cognitive processing, ranging from stimulus processing to peripheral nondecision processes. Thus, sleep deprivation appears to have wide-ranging effects: Reduced attentional arousal and impaired central processing combine to produce an overall decline in cognitive functioning.