Unit 11.1A · Term 1

Boolean Logic & Gates

At the hardware level, every computation is about true/false (1/0) decisions. Logic gates are the physical building blocks that perform these Boolean operations inside every CPU.

Learning Objectives

11.3.3.3 Build truth tables for AND, OR, NOT, NAND, NOR, XOR

Lesson Presentation

11.1A-boolean-logic.pdf · Slides for classroom use

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Conceptual Anchor

The Light Switch Analogy

AND gate = two switches in series (BOTH must be ON for the light to turn on). OR gate = two switches in parallel (EITHER one turns the light on). NOT gate = an inverter (if switch is ON, light is OFF and vice versa).

Rules & Theory

Logic Gate Summary

Gate	Symbol	Rule	Expression
AND	A · B	Output 1 only if BOTH inputs are 1	Q = A AND B
OR	A + B	Output 1 if ANY input is 1	Q = A OR B
NOT	Ā or ¬A	Output is the OPPOSITE of input	Q = NOT A
NAND	A · B̄	Opposite of AND (NOT AND)	Q = NOT (A AND B)
NOR	A + B̄	Opposite of OR (NOT OR)	Q = NOT (A OR B)
XOR	A ⊕ B	Output 1 if inputs are DIFFERENT	Q = A XOR B

Truth Tables

NOT (1 input):          AND (2 inputs):         OR (2 inputs):
 A │ Q                   A  B │ Q                 A  B │ Q
───┼───                 ─────┼───               ─────┼───
 0 │ 1                  0  0 │ 0                 0  0 │ 0
 1 │ 0                  0  1 │ 0                 0  1 │ 1
                         1  0 │ 0                 1  0 │ 1
                         1  1 │ 1                 1  1 │ 1

NAND:                   NOR:                    XOR:
 A  B │ Q               A  B │ Q                A  B │ Q
─────┼───             ─────┼───              ─────┼───
 0  0 │ 1              0  0 │ 1               0  0 │ 0
 0  1 │ 1              0  1 │ 0               0  1 │ 1
 1  0 │ 1              1  0 │ 0               1  0 │ 1
 1  1 │ 0              1  1 │ 0               1  1 │ 0

Memory Tricks

Gate	Memory Aid
AND	"Both must agree" — 1 AND 1 = 1
OR	"At least one" — any 1 makes output 1
NOT	"Flip it" — 0→1, 1→0
NAND	"Not AND" — flip the AND output
NOR	"Not OR" — flip the OR output
XOR	"eXclusive" — different inputs = 1, same = 0

NAND: The Universal Gate

Any logic circuit can be built using only NAND gates. This is why NAND is called a "universal gate". In practice, NAND-based chips are cheaper to manufacture, so most integrated circuits use NAND gates internally.

Worked Examples

1 Build a Truth Table for (A AND B) OR C

 A  B  C │ A AND B │ (A AND B) OR C
────────┼────────┼───────────────
0  0 │   0    │      0
0  1 │   0    │      1
1  0 │   0    │      0
1  1 │   0    │      1
0  0 │   0    │      0
0  1 │   0    │      1
1  0 │   1    │      1
1  1 │   1    │      1

Common Pitfalls

XOR = OR

OR outputs 1 when A=1, B=1. XOR outputs 0 when both are 1 (it means "exclusively one or the other, not both").

Tasks

Remember

Draw the truth tables for all 6 gates: AND, OR, NOT, NAND, NOR, XOR.

Apply

Build a truth table for: (A OR B) AND (NOT C)

Analyze

Explain why NAND is called a "universal gate". Show how to create NOT using only NAND.

Self-Check Quiz

Q1: What is the output of 1 AND 0?

0 — AND requires BOTH inputs to be 1.

Q2: What is the output of 1 XOR 1?

0 — XOR outputs 1 only when inputs are DIFFERENT.

Q3: What gate gives the opposite output of OR?

NOR (NOT OR).