Part IV: Digital Electronics
Boolean algebra, combinational logic, sequential circuits, flip-flops, counters, and finite state machines — the foundations of every processor, controller, and digital system.
The Digital Abstraction Stack
What You Will Learn
Digital electronics operates on binary signals — voltages that represent only two states, logic HIGH (1) and logic LOW (0). This discretization is the fundamental insight that allows noise to be rejected and computations to be performed reliably even with imperfect components.
The mathematics of digital logic is Boolean algebra, where variables take values in\( \{0, 1\} \) and operations are AND (\( \cdot \)), OR (+), and NOT (\( \overline{\phantom{A}} \)). De Morgan's theorems connect these:
Sequential logic adds memory to combinational circuits — flip-flops store single bits and, combined into registers and counters, form the state-holding elements of every digital system. Finite state machines (FSMs) provide the formal framework for designing complex sequential controllers.
Combinational vs Sequential Logic
Output depends only on current inputs. No memory. Examples: adders, multiplexers, decoders, encoders, logic gates.
Output depends on current inputs AND past history (state). Examples: flip-flops, registers, counters, FSMs, memories.
Chapters in Part IV
Boolean Algebra & Logic Gates
AND, OR, NOT, NAND, NOR, XOR gates, De Morgan's theorems, truth tables, Karnaugh maps, sum-of-products and product-of-sums minimization.
Flip-Flops & Counters
SR latch, D, JK, and T flip-flops, timing diagrams, synchronous vs asynchronous counters, binary, ring, and Johnson counters.
Finite State Machines
Mealy vs Moore machines, state diagrams, state tables, state encoding, FSM design procedure with traffic light controller example.