Logic and Gates
Digital logic is built from a small set of Boolean operations. Complex processors ultimately reduce to enormous networks of these simple functions.
NOT
A NOT gate, or inverter, produces the opposite logic state.
AND
The output is HIGH only when all required inputs are HIGH.
OR
The output is HIGH when at least one input is HIGH.
NAND and NOR
NAND is an AND followed by inversion. NOR is an OR followed by inversion. Either NAND gates alone or NOR gates alone can be used to construct every other Boolean logic function, making them universal gates.
XOR and XNOR
Exclusive-OR is HIGH when inputs differ. XNOR is HIGH when inputs are equal. XOR is useful in arithmetic, parity generation, controlled inversion, and comparison.
De Morgan's laws
NOT(A + B) = (NOT A) · (NOT B)
These identities are important when translating a logic function into NAND- or NOR-based hardware.
Active-low signals
A control line may perform its function when LOW rather than HIGH. Datasheets indicate this with a bar over the signal name, a slash, a trailing N, or another naming convention.
RESET, /RESET, RESET_N, and an overbarred RESET can all mean roughly the same thing: the function is asserted at logic 0.
Don't-care conditions
Some truth-table combinations either cannot occur or do not matter to the desired output. These can be marked X and used to simplify Boolean expressions.
Karnaugh maps
Karnaugh maps provide a visual method of simplifying small Boolean functions without formal algebra. They are especially useful when learning how gate count can be reduced.
Logic diagrams versus real hardware
A gate symbol hides transistor-level details, current limits, propagation delay, input capacitance, thresholds, and power-supply requirements. Digital design works well because those analog details are kept inside defined limits.