We used both student interviews and diagnostic testing to reveal students' misconceptions about number representations in computing systems. This article reveals that students who have passed an undergraduate level computer organization course still possess surprising misconceptions about positional notations, two's complement representation, and overflow. Contrary to common opinion, these misconceptions are widespread and reveal the need for instruction that specifically targets these misconceptions. In addition, these misconceptions will serve as the basis for the creation of a standard assessment tool called the digital logic concept inventory. This concept inventory will provide a rigorous and quantitative metric to assess the effectiveness of new teaching methods. (Contains 1 figure.)