Logic gates and truth tables

Six gates

NOT inverts. AND outputs 1 only when both inputs are 1. OR outputs 1 when at least one input is 1. NAND and NOR are AND and OR followed by NOT. XOR outputs 1 when the inputs differ — read it as "one or the other but not both".

Notation you must be able to switch between

$\overline{A}$ for NOT $A$; $A\cdot B$ (or $AB$) for AND; $A+B$ for OR; $A\oplus B$ for XOR. Exam questions move freely between logic diagrams, Boolean expressions and truth tables, and a large share of the marks is simply translating between the three without error.

Building a truth table properly

List inputs in binary counting order — $00,01,10,11$ for two inputs, eight rows for three. Then add one column per intermediate signal, not just the final output. Working column by column is what stops mistakes in a circuit with four gates, and examiners award marks for correct intermediate columns.

Reading a circuit

Work left to right, labelling the output of every gate before moving on. If a wire branches, the same signal feeds both destinations — a branch is not a new variable.

NAND and NOR are universal

Any circuit can be built from NAND gates alone (or NOR gates alone), which matters commercially: manufacturing one gate type is cheaper than manufacturing six.