Boolean Logic Masterclass

J277 Specification Reference: 2.4 Boolean logic

Learning Objectives

Recognise and draw standard logic gate symbols (AND, OR, NOT). Complete truth tables for 2-input and 3-input logic systems. Create, complete and edit logic diagrams from scenarios. Apply logical operators to solve problems.

Why this matters

Computers make decisions using simple True/False rules, just like strict parents.

Rule 1: AND (Strict)

"You can play if you have finished homework AND tidied your room."

Homework + Room = Play

Rule 2: OR (Relaxed)

"You can play if it is the weekend OR if it is a holiday."

Weekend = Play

1. Core Knowledge: The Gates

Tap cards to flip

AND

Tap for definition

AND Gate

Output is 1 only if BOTH inputs are 1.

Also called: Conjunction

OR

Tap for definition

OR Gate

Output is 1 if EITHER (or both) inputs are 1.

Also called: Disjunction

NOT

Tap for definition

NOT Gate

Output is the INVERSE (opposite) of the input.

Warning: Don't forget the circle!

Examiner's Eye: Sloppy Drawings

Marks are frequently lost for drawing the OR gate with a straight back (making it look like a D-shape AND gate). Make the curve obvious.

Examiner's Eye: Missing Circle

A triangle without the small circle at the end is just a "buffer"—it does nothing to the signal. No circle = zero marks for a NOT gate.

Checkpoint 1

I can recognise and name the 3 logic gates.

Logic Lab

Choose Gate:

Input A 0

Input B 0

AND Gate

2. Mastering Truth Tables

Examiner's Eye: Mixing Notation

Never mix 1/0 and True/False in the truth table. Pick ONE style (ideally 1s and 0s) and stick to it strictly.

The AND Rule

Output is 1 only if A AND B are 1.

Exam Tip: Inputs always count up in binary: 00, 01, 10, 11.

A	B	Output Q
0	0	?
0	1	?
1	0	?
1	1	?

The OR Rule

Output is 1 if there is a 1 anywhere in the inputs.

A	B	Output Q
0	0	?
0	1	?
1	0	?
1	1	?

The NOT Rule

Simply flips the input.

A	Output Q
0	?
1	?

The 8-Row Challenge

Many exam questions use 3 inputs (A, B, and C). This means you need 8 rows ($2^3=8$) to cover every combination.

Task: Complete the table for P = (A AND B) OR C

Examiner Technique: Add a "Working Out" column for the intermediate gate (A AND B) before trying to calculate the final output.

A	B	C	Working: (A AND B)	Output P
0	0	0	0	0
0	0	1	0	1
0	1	0	0	0
0	1	1	0	1
1	0	0	0	0
1	0	1	?	?
1	1	0	?	?
1	1	1	?	?

Hint: If (A and B are 1) OR (C is 1), the result is 1.

Checkpoint 2

I can complete truth tables for 2 and 3 inputs.

Diagram Bootcamp

How to Decompose a Question

Exam Question: "The Alarm (Q) sounds if the Motion Sensor (A) is on, AND the System is Armed (B), OR if the Panic Button (C) is pressed."

Step 1: Find the 'Bracket'

"Motion AND Armed" belong together. Draw an AND gate for A and B first.

Step 2: Connect the Result

Take the output line from that gate, and plug it into an OR gate along with input C.

Scenario: The Garden Floodlight

"The light (Q) turns on if the Switch is ON (C) AND motion is detected (A) at Night (NOT B)."

Checkpoint 3

I can create and edit diagrams from written scenarios.

Final Assessment

1. Which symbol represents a NOT gate?

2. Reverse Engineering

Look at this truth table. Which gate produces this output?

A	B	Output
0	0	0
0	1	1
1	0	1
1	1	1

3. Logic Tracing

System: P = NOT A AND (B OR C).
If A=1, B=1, C=1, what is P?

Hint: Work out NOT A first.

Checkpoint 4

I can apply logical operators to solve problems.