The Atoms of Computation
Every digital device — from a pocket calculator to a supercomputer — is built from a small set of logic gates. These gates take binary inputs (0 or 1) and produce a binary output according to a fixed Boolean function. The AND gate outputs 1 only when both inputs are 1. The OR gate outputs 1 when at least one input is 1. The NOT gate simply inverts its single input. From these primitives, all of digital computing is constructed.
Universal Gates
A remarkable fact of Boolean algebra is that the NAND gate alone can implement any logical function. By combining NAND gates in different configurations, you can build AND, OR, NOT, XOR, and every other gate. This universality is why real-world chip fabrication often uses NAND-only or NOR-only libraries — it simplifies manufacturing while retaining full computational power.
From Gates to Circuits
Individual gates are combined into larger circuits: multiplexers route data, decoders select memory addresses, and arithmetic logic units (ALUs) perform addition and subtraction. Each layer of abstraction builds on the layer below. The half adder you can explore in another simulation is just an XOR gate and an AND gate working together.
Propagation and Timing
In physical circuits, signals don't change instantaneously. Each gate introduces a tiny propagation delay — typically a few picoseconds in modern silicon. When gates are chained, these delays accumulate, forming the critical path that determines a processor's maximum clock speed. Understanding gate-level timing is essential for designing fast, reliable digital systems.