The multiple-choice question (MCQ) is the foundation of knowledge assessment in K-12, higher education, and standardized entrance exams (including the GRE, MCAT, and DAT). However, standard MCQ exams are limited with respect to the types of questions that can be asked when there are only five choices. MCQs offering additional choices more extensively test an examinee's knowledge of complex concepts and thus an examiner can get a more accurate assessment of the examinee's comprehension. We introduce an assessment paradigm in which choices of the MCQs are items in an array encoded with a number that can be expressed via binary notation in the standard five-choice MCQ answer sheet. Numbers can be represented by combinations of zeroes (unfilled bubbles) and ones (filled bubbles) at each of the five numerical place-holder positions. A scanner that recognizes five filled/unfilled "bubbles" per horizontal line of the answer sheet makes it possible to represent 31 options as possible answers. The rubric provides a more comprehensive assessment of a student's knowledge than a standard five-choice MCQ. It has the potential to revolutionize MCQ testing. We present examples of MCQ assessment of chemical concepts at all levels of Bloom's taxonomy, employing item arrays and binary-coded choices.