We represent binary signals in digital systems as high voltage (1), and low voltage (0) signals.
For example, Arduino reads 3-5V as HIGH, or true and 0.-1.5V as LOW or false.
Note: Other than NOT gate, logic gates can have more than two inputs
A boolean function described by a boolean expression has binary variables, and constants 0, and 1, and logic operation symbols. The function must return a value of either 0, or 1. eg. $F = x + y.z$
Boolean functions can be represented as a truth table, and the number of rows is given by $2^n$, where n is the number of variables in the function. For each boolean function we have one, and only one, truth table. Multiple algebraic forms may have the same truth table; in that case they are equivalent statements or functions.
By manipulating a boolean expression according to the rules of boolean algebra, it is sometimes possible to obtain simpler expressions, reducing the complexity of the circuit representing it.
The complement of a function F is the function such that it outputs 0 when F outputs 1, and vice versa. We can also derive the complement algebraically:
The generalized form of DeMorgan’s theorem states that you can
A minterm is a standard product, for $n$ binary variables, we can have $2^n$ possible minterms.
For eg. with variables x and y
Similarly we have maxterms, which are standard sums.
For eg. with variables x and y