Understand the logic gates NOT, AND, OR, XOR, NAND and NOR, their truth tables, combining gates into logic circuits, and simplifying expressions using Boolean algebra.

What this dot point is asking

AQA wants you to know the logic gates and their truth tables, build and read combinational logic circuits, write Boolean expressions for them, and simplify expressions using the laws of Boolean algebra including De Morgan's laws.

The logic gates

A truth table lists every combination of inputs and the resulting output. For two inputs there are $2^2 = 4$ rows; for $n$ inputs there are $2^n$ rows, which is why three-input circuits have eight rows.

A B | AND  OR  XOR
0 0 |  0    0    0
0 1 |  0    1    1
1 0 |  0    1    1
1 1 |  1    1    0

NAND and NOR are described as universal gates because any other gate, and so any circuit, can be built from NAND alone or from NOR alone. This matters in hardware manufacture because building a chip from a single repeated gate type is simpler and cheaper, which is why this property is worth knowing even though the exam mainly tests the basic six.

Logic circuits and Boolean expressions

Gates are wired together to form a combinational logic circuit whose output depends only on the current inputs (unlike sequential circuits, which also depend on stored state). Each circuit corresponds to a Boolean expression, for example $Q = (A \cdot B) + \overline{C}$, and you can move freely between three equivalent representations: the circuit diagram, the Boolean expression, and the truth table. A common exam task is to be given one and produce another, for example reading a circuit to write its expression, or building a truth table from an expression by evaluating it for every input row.

Simplifying with Boolean algebra

For example, $A \cdot B + A \cdot \overline{B} = A \cdot (B + \overline{B}) = A \cdot 1 = A$, so a circuit that looks like it needs three gates reduces to a plain wire. The practical reason this matters is that fewer gates means a smaller, cheaper, faster chip, so simplification is not an academic exercise but a real engineering goal. De Morgan's laws are the most error-prone: the rule is that when a bar is broken across an expression, the operator underneath it flips (AND to OR, OR to AND) and each variable is individually inverted.