Perceptron
The simplest neural network, a linear binary classifier: it computes w·x + b and outputs 1 if the result is positive, else 0. It learns by nudging its weights toward every example it gets wrong.
ŷ = step(w·x + b)
Example
With weights (1, 1) and bias −1.5, a perceptron computes logical AND: only the input (1, 1) gives 1 + 1 − 1.5 > 0.