What is Boolean Logic?

Boolean logic is a system of logic based on only two possible values: True or False — represented in computing as 1 (True) and 0 (False). It was developed by mathematician George Boole in the 19th century and is fundamental to how computers process decisions and data.

Every decision a computer makes — from checking a password to displaying a webpage — ultimately reduces to Boolean logic. Processors work using billions of tiny switches (transistors) that are either on (1) or off (0), making Boolean logic the language of hardware itself.

• Boolean values: True / False or equivalently 1 / 0
• Used in conditions, loops, and decision-making in programs
• The basis of all digital circuit design

The Three Basic Boolean Operators

Edexcel 1CP2 requires you to know three Boolean operators: AND, OR, and NOT. Each takes Boolean inputs and produces a Boolean output.

AND Operator

The AND operator returns True only when ALL inputs are True. If any input is False, the result is False. Think of it as: "both conditions must be met."

Example: A door unlocks if the card is valid AND the PIN is correct. Both must be True.

OR Operator

The OR operator returns True when AT LEAST ONE input is True. It only returns False when all inputs are False. Think of it as: "at least one condition must be met."

Example: An alarm triggers if motion is detected OR a window is broken. Either condition is enough.

NOT Operator

The NOT operator takes a single input and inverts it. True becomes False, and False becomes True.

Example: A light turns on if the room is NOT already lit.

Combining Operators

Boolean operators can be combined to create more complex logic expressions. When evaluating combined expressions, work from the inside out — resolve brackets first, then apply outer operators.

Worked Example: NOT(A AND B)

This expression first evaluates A AND B, then inverts the result using NOT.

Notice that NOT(A AND B) is only False when both A and B are True.

Truth Tables

A truth table is a systematic table that lists every possible combination of inputs and their corresponding output for a Boolean expression. Truth tables are the standard way to prove how a logic expression behaves.

Two-Input Truth Tables (4 rows)

With 2 inputs (A and B), there are 4 possible combinations: 00, 01, 10, and 11. Always list them in this order to be systematic.

Three-Input Truth Tables (8 rows)

With 3 inputs (A, B, C), there are 8 possible combinations (2³ = 8). List them systematically — C alternates every row, B alternates every 2 rows, A alternates every 4 rows.