22-Elec-A4 Digital Systems and Computers, May 2013: worked solutions

Paper format. National Exams, May 2013 — 07-Elec-A4 Digital Systems & Computers. Three hours, closed book (one approved Casio or Sharp calculator). Six questions are printed; any five constitute a complete exam and all questions are worth 12 marks. An excitation table for the RS/JK/T/D flip-flops and a table of basic Boolean identities are supplied on the last page of the paper. All six questions are solved below, because this set is a study resource rather than a timed sitting.

Reference texts.

M. M. Mano and M. D. Ciletti, Digital Design: With an Introduction to the Verilog HDL, VHDL, and SystemVerilog, 6th ed. — Boolean algebra (Ch. 2), combinational design (Ch. 4), synchronous sequential logic (Ch. 5), registers and counters (Ch. 6), memory and address decoding (Ch. 7).
J. F. Wakerly, Digital Design: Principles and Practices, 5th ed. — canonical forms and minimisation (Ch. 3–4), counters and shift registers (Ch. 8).
C. Hamacher, Z. Vranesic, S. Zaky and N. Manjikian, Computer Organization and Embedded Systems, 6th ed. — bus structure and addressing (Ch. 2), stacks (§2.6), memory system organisation and chip-select decoding (Ch. 8).

Convention used throughout. In the address/data expressions a prime denotes complement ($\overline{A}$ is written A′ in the figures, where SVG text cannot carry an overbar). Hexadecimal constants keep the Motorola dollar-sign notation of the exam paper, written here as $7A01 in prose so that it cannot be mistaken for a mathematics delimiter.

22-Elec-A4 Digital Systems and Computers: May 2013