Digital logic gates process binary inputs to produce output signals by performing logical operations on the given inputs. The most common logic gates are AND, OR, NOT, NAND, NOR, and XOR gates. Each gate follows specific logical rules to determine the output based on the input signals. For example, an AND gate produces a high output signal only if all its input signals are high, while an OR gate produces a high output if any of its input signals are high. By combining these gates in various configurations, complex digital circuits can be created to perform specific functions.