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Logic Gates and Logic Circuits
Logic gates are simple electronic circuits that take one or more binary inputs and produce a single binary output. By combining these gates, we can build complex systems that perform everything from simple arithmetic to running a full operating system.
Need to know
What you need to know
- **NOT Gate:** Has one input and one output. It inverts the input. If input A is 1, output X is 0. If A is 0, X is 1. Boolean expression: $X = \neg{A}$.
- **AND Gate:** Has two or more inputs and one output. The output is 1 only if *all* inputs are 1. Boolean expression: $X = A \cdot B$.
- **OR Gate:** Has two or more inputs and one output. The output is 1 if *any* input is 1. Boolean expression: $X = A + B$.
Explanation
The Building Blocks of Logic
- Basic gates like NOT, AND, and OR have defined behaviours. Their output for every possible combination of inputs is captured in a truth table.
- NAND and NOR gates are 'universal'. This means you can construct any other logic gate, and therefore any logic circuit, using only NAND gates or only NOR gates.
- Boolean algebra is the mathematics used to analyse and simplify logic circuits. Key rules, like De Morgan's laws, allow us to find equivalent circuits with fewer gates, saving cost and power.
- Logic circuits are combinations of gates designed to perform specific tasks. These range from simple adders in a CPU to complex control logic in memory systems.