Logic Circuits
Gates and Boolean algebra
Learn the truth tables for AND, OR, NOT, NAND, NOR, XOR and XNOR, and be able to read a symbol as an equation. NAND and NOR are universal: any function can be built from either alone. De Morgan's theorems - NOT(A AND B) = NOT A OR NOT B, and NOT(A OR B) = NOT A AND NOT B - appear constantly.
Combinational versus sequential
Combinational circuits have no memory: adders, comparators, encoders, decoders, multiplexers. Sequential circuits store state: latches, flip-flops (SR, JK, D, T), registers, counters and shift registers. They are synchronous (clocked) or asynchronous, and edge-triggered devices need data stable around the clock edge - set-up and hold times.
Practical points
Fan-out is how many inputs one output can drive; propagation delay limits speed; tri-state outputs allow shared buses provided only one is enabled at a time. Unused inputs must never float - tie them to a defined level, especially on CMOS. Memory: RAM is volatile, while ROM, PROM, EPROM, EEPROM and flash keep their contents without power.
Traps
Forgetting that XOR gives 1 only when inputs differ; drawing a NAND with the bubble on an input instead of the output; assuming a correct truth table proves the circuit works when the fault is timing or loading.
Worked example
The sum output of a half-adder is A XOR B. Build the truth table first, simplify with Boolean algebra or a Karnaugh map, and select gates last - this order avoids most mistakes.