DL · Section 2: Digital Logic
Digital Logic
Boolean algebra, combinational and sequential circuits, minimization, number representations and computer arithmetic.
Topics
6 topics in syllabus order, each with study material.
Positional systems and base conversion (integer and fraction parts, grouping for octal and hex, unknown-base equations), unsigned, sign-magnitude, 1's and 2's complement ranges and readings, r's and (r-1)'s complements, sign extension, excess-K, and the codes BCD, excess-3, 2421 and Gray with BCD addition.
Laws and theorems with their duals, De Morgan, absorption, consensus, XOR algebra and algebraic simplification; minterms and maxterms, canonical SOP and POS, duals and complements in index form; counting Boolean, self-dual and other function classes; functional completeness by Post's five classes, NAND and NOR realisations and minimum gate counts.
Karnaugh maps for 2 to 5 variables in Gray order, grouping rules, prime and essential prime implicants, don't-cares, minimal SOP and POS, and the Quine-McCluskey tabular method with the prime-implicant chart, row and column reduction and Petrick's method for cyclic charts.
Half and full adders and subtractors, ripple-carry and carry-lookahead delay with generate and propagate, adder-subtractor, comparators, multiplexers and implementing functions with them, mux and decoder trees, decoders, encoders and priority encoders, static hazards, and ROM sizing.
SR, D, JK and T latches and flip-flops with characteristic and excitation tables, level versus edge triggering, setup, hold and maximum clock frequency, shift registers, ripple, synchronous, mod-N, ring and Johnson counters, counter design and lockout, Moore and Mealy machines, state minimisation and sequence detectors.
Two's complement addition and subtraction with carry, overflow and flag rules, shifts and fixed-point (Q) formats, shift-and-add and Booth multiplication, restoring and non-restoring division, and IEEE 754 single and double: fields, bias, normal and subnormal values, zero, infinity, NaN, range, precision, encoding, addition and rounding.
Digital Logic revision: traps, patterns and last day
Digital Logic revision: the traps sheet with wrong turn, correct rule and fix; the question-pattern sheet from stem cue to method and check; and the master last-day sheet with the formulas, tables and conventions of the whole pack.