I investigate how and whether a heterogeneous group of first-year university mathematics students in South Africa harness the potential power of a computer algebra system (CAS) when doing a specific mathematics task. In order to do this, I develop a framework for deconstructing a mathematics task requiring the use of CAS, into its primary components. This framework is based on the semiotic notion of diagrammatic reasoning whereby reasoning consists of construction of signs, transformation of signs, and observation and interpretation of signs. I use the framework to distinguish between the activities of students who were computer literate on entry to university and those who were not computer literate. The analysis suggests that formerly non-computer literate students are no worse than computer literate students in using CAS to construct various representations of signs, but that they are less able to interpret these signs. I propose that, in the South African context, this is largely due to inequities in prior mathematical education, rather than a lack of computer literacy per se. (Contains 5 tables and 7 figures.)