Of the boolean logic functions possible, we only consider a few of them as standard logic gates, owing to practical reasons.
We do not consider any of the unary operations, such as NOT
The inhibition and implication functions are not associative or commutative, thus we do not consider them either.
The AND, OR, NOT, XOR, NAND, NOR
Universal gates
The NAND and the NOR gates are known as universal gates, any logic gate can be constructed using either one of these gates.
We can show this by implementing NOT, AND and OR gates, which are known as the basic gates. If we can implement these basic gates,
then we can implement any digital circuit.
NOT: For a signal $x$, we can get $x’$ by doing either $(x.x)’$ or $(x.1)’$.
AND: Now that we have a NOT gate, we can implement AND by putting this NOT gate after the AND gate, giving us $((x.y)’)’$ = $(x.y)$.
OR: Using DeMorgan’s law, we know that $(x.y)’ = (x’ + y’)$. We can use this fact to generate and OR gate as follows $(x’.y’)’ = ((x’)’ + (y’)’) = (x + y).
Timing diagrams
The horizontal axis in a timing diagram represents the time, and the vertical axis shows the signal as it changes between the two possible voltage levels. By interpreting the signal as the output values of a truth table, this information can be carried in the signal.