Digital Logic Design
Logic design lives in waveforms, not in prose. These topics drive real inputs through gates, latches and counters, and show the outputs settle.
Start from the beginning →8 topics you can watch now, 16 still to come.
Foundations
Why a computer is built out of two voltages, and the handful of gates that is all you get.
- Why Digital, and Why BinaryStart here. Send one value down a noisy wire as a level and as a bit, and only one of them survives.
- Logic Gates and Truth TablesSeven gates, seven truth tables — and the proof that you only ever needed one of them.
- Positive and negative logic
- Fan-in, fan-out and propagation delay
Number systems
Every value a circuit holds is a pattern of bits you chose.
- Counting in Any BaseWatch the column weights re-scale from 1000-100-10-1 to 8-4-2-1, and hex stops being a separate system.
- Signed Numbers and Two's ComplementThree ways to write −5, and only one of them lets the adder you already built be correct.
- BCD and Gray code
- Floating point representation
Combinational logic
Output depends only on input, right now, with no memory.
- Boolean Algebra and De Morgan's LawsFour lines of algebra turn a three-gate circuit into a piece of wire — and De Morgan drawn as two schematics.
- K-map SimplificationGroup the ones and watch variables cancel. Includes the wrap-around groups everybody misses.
- Adders and Carry PropagationFollow the carry across four stages one gate delay at a time, and see exactly why lookahead exists.
- Multiplexers and DecodersMove the select lines and watch the route move — then wire a truth table into the data inputs.
- Quine-McCluskey
- Comparators and parity generators
Sequential logic
Add a clock and a feedback path, and the circuit can remember.
- SR, JK, D and T flip-flops
- Setup and hold timing
- Registers and shift registers
- Synchronous counters
State machines
Designing behaviour as states first, then as a circuit.
- Moore vs Mealy
- State diagram to circuit
- State minimisation
Memory and logic families
How a bit is physically stored, and what that costs.
- ROM, PLA and PAL
- SRAM vs DRAM cells
- TTL and CMOS
About Digital Logic Design
Digital logic is the bridge between physics and computation. It starts with a decision that looks almost arbitrary — treat a range of voltages as zero and another as one — and shows how that single abstraction lets you build arithmetic, memory and eventually a processor out of switches.
Two halves follow. Combinational logic has no memory: outputs depend only on current inputs, and the work is in expressing a function with fewer gates, which is what Boolean algebra and Karnaugh maps are for. Sequential logic adds state, and with it timing — setup, hold, clocking — and a whole new category of things that can go wrong.
This is the foundation the rest of computer hardware stands on. Adders, multiplexers and decoders reappear inside processors, memory controllers and every microcontroller peripheral, so the effort spent here is not spent once.
What to know first
- Nothing beyond arithmetic — this is where the hardware story starts
- Familiarity with binary helps but is built up here anyway
Where it gets used
- Reading a datasheet timing diagram and knowing what constraint it states
- Understanding why fixed-width integers overflow the way they do
- Following how an instruction becomes control signals inside a CPU