22-Elec-A4 Digital Systems and Computers, May 2014: worked solutions

Paper format. National Exams, May 2014 — 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 every question is worth 12 marks, with the per-part split given in the page-1 marking scheme (Q1 is 3+3+3+3; Q2 is 6+3+3; Q3 is 6+6; Q4 is 3+3+6; Q5 and Q6 are 4+4+4). A flip-flop excitation table for the RS/JK/T/D types and a table of 22 basic Boolean identities are supplied on the last page. 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, canonical forms and K-maps (Ch. 2–3), combinational MSI decoders and demultiplexers (Ch. 4), synchronous sequential design and flip-flop excitation (Ch. 5), registers and counters (Ch. 6).
J. F. Wakerly, Digital Design: Principles and Practices, 5th ed. — minimisation and static timing hazards (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. — the four essential subsystems and bus structure (Ch. 1–3), serial interfaces and UART framing (§3.5), the processor register set and addressing modes (Ch. 2).
M. A. Mazidi, R. McKinlay and D. Causey, PIC Microcontroller and Embedded Systems — port-driven multiplexed seven-segment displays and LED current limiting (Ch. 12).

Notation used throughout. A bar and a prime both denote complement: \(\overline{A}\) in the mathematics and A′ in the figures, where SVG text cannot carry an overbar. In every K-map the leftmost variable is the most significant bit, so the minterm indices printed in the cells match the question’s own variable ordering.

22-Elec-A4 Digital Systems and Computers: May 2014