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

Paper format. National Exams, December 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 every question is worth 12 marks, with the per-part split printed in the marking scheme on page 1 (Q1 and Q5 are 3+3+3+3; Q2 is 4+4+4; Q3 and Q6 are 6+6; Q4 is 8+2+2). An excitation table for the RS/JK/T/D flip-flops 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 and K-maps (Ch. 2–3), combinational MSI design with multiplexers and decoders (Ch. 4), synchronous sequential logic and flip-flop excitation (Ch. 5), registers and counters (Ch. 6), memory and programmable logic (Ch. 7).
J. F. Wakerly, Digital Design: Principles and Practices, 5th ed. — canonical forms, minimisation and timing hazards (Ch. 3–4), PLD architectures (Ch. 5), counters (Ch. 8).
C. Hamacher, Z. Vranesic, S. Zaky and N. Manjikian, Computer Organization and Embedded Systems, 6th ed. — bus structure and I/O (Ch. 3), polling versus interrupts (§3.2), serial interfaces (§3.5), memory system organisation and chip-select decoding (Ch. 8).

Notation used throughout. A prime and an overbar both denote complement: \(\overline{A}\) in the mathematics, A′ in the figures, where SVG text cannot carry an overbar. The variable order in every K-map is the order printed in the question, with the leftmost variable as the most significant bit, so minterm and maxterm indices match the question's numbering exactly.

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