State the function, symbol, truth table and Boolean expression of the AND, OR and NOT logic gates

What this dot point is asking

SEAB wants you to state the function, symbol, truth table and Boolean expression of the three basic logic gates: AND, OR and NOT. The central insight is that each gate is a simple rule connecting one or two binary inputs to a binary output, and that the truth table lists the output for every possible combination of inputs. These three gates are the alphabet of all digital logic.

The answer

The AND gate

An AND gate has two (or more) inputs and one output. Its output is logic 1 only when all of its inputs are logic 1; otherwise the output is 0. Think of two switches in series: the lamp lights only when both are closed. The Boolean expression is:

Truth table: $00 \to 0$, $01 \to 0$, $10 \to 0$, $11 \to 1$.

The OR gate

An OR gate has two (or more) inputs and one output. Its output is logic 1 when at least one input is logic 1; the output is 0 only when all inputs are 0. Think of two switches in parallel: the lamp lights if either is closed. The Boolean expression is:

Truth table: $00 \to 0$, $01 \to 1$, $10 \to 1$, $11 \to 1$.

The NOT gate

A NOT gate, also called an inverter, has a single input and one output. It simply reverses the input: an input of 0 gives an output of 1, and an input of 1 gives an output of 0. The Boolean expression uses a bar over the input:

Truth table: $0 \to 1$, $1 \to 0$.

Reading the symbols and tables

Each gate has a standard symbol: the AND gate has a flat back and a round front (a D shape), the OR gate has a curved back and a pointed front, and the NOT gate is a triangle with a small circle (the "bubble") on its output that means invert. A truth table must list every input combination: two inputs give four rows, and one input gives two rows. Always work through the rows in the standard binary order so none is missed.

Examples in context

Example 1. A safety interlock with AND. A machine should only run when the guard is closed AND the start button is pressed. Feeding both conditions into an AND gate means the machine starts only when both are true, exactly matching the AND truth table. This is a common safety use of a single gate.

Example 2. An alarm with OR. A burglar alarm should sound if the door sensor OR the window sensor is triggered. An OR gate gives an output of 1 whenever either input is 1, so the siren sounds if either entry point is disturbed. One gate captures the "either one" logic cleanly.

Try this

• Cue. State the output of an AND gate when its inputs are 1 and 1. AND gives 1 only when both inputs are 1, so the output is 1.

• Cue. Write the Boolean expression for an OR gate with inputs $X$ and $Y$. $Q = X + Y$, where the plus means OR.

• Cue. A NOT gate has an input of 0. State its output. The NOT gate inverts its input, so an input of 0 gives an output of 1.