Lesson 1: Understanding Binary - From 0 and 1 to the Computer World

📌 Learning Objectives

1. Understand what binary is
2. Master conversion between decimal and binary
3. Understand the role of binary in microcontrollers
4. Experience practical applications of binary through experiments

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🎯 What is Binary?

Review of Decimal

We use decimal in daily life, which has 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

Rule: Carry over when reaching 10

  15
+  8
----
  23

Introduction to Binary

Computers use binary, which has only 2 digits: 0 and 1.

Rule: Carry over when reaching 2

  101
+   1
----
  110

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🔄 Decimal ↔ Binary Conversion

Decimal → Binary: Divide by 2, Collect Remainders

Example: Convert decimal 13 to binary

13 ÷ 2 = 6  remainder 1  ← least significant bit
6  ÷ 2 = 3  remainder 0
3  ÷ 2 = 1  remainder 1
1  ÷ 2 = 0  remainder 1  ← most significant bit

Result: 1101

Binary → Decimal: Weighted Sum

Example: Convert binary 1011 to decimal

1    0    1    1
↓    ↓    ↓    ↓
2³   2²   2¹   2⁰
8    4    2    1

8 + 0 + 2 + 1 = 11

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💡 The Meaning of Binary in Microcontrollers

1. Representing Switch States

• 0 = OFF
• 1 = ON

2. Representing Logic

• 0 = False
• 1 = True

3. Register Storage

Microcontroller registers store data in binary!

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🔬 Classroom Demo: Binary LED Array

Experiment Goal

Use 4 LEDs to represent a 4-bit binary number, counting from 0 to 15.

Hardware Connections

LED	Connection	Binary Bit
LED1	Output 0	2⁰ (1)
LED2	Output 1	2¹ (2)
LED3	Output 2	2² (4)
LED4	Output 3	2³ (8)

Example Code

; Count from 0 to 15, display binary with LEDs
000 01 0000 0000  ; 0 (0000)
001 02 03E8 0000  ; delay
002 01 0001 0000  ; 1 (0001)
003 02 03E8 0000  ; delay
004 01 0002 0000  ; 2 (0010)
005 02 03E8 0000  ; delay
006 01 0003 0000  ; 3 (0011)
007 02 03E8 0000  ; delay
008 0E 0000 0000  ; loop

Teaching Suggestions

Ask students to guess what the next number will be, or let them design their own counting program.

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📊 Common Decimal-Binary Conversion Table

Decimal	Binary	Hex
0	0000	0x00
1	0001	0x01
2	0010	0x02
3	0011	0x03
4	0100	0x04
5	0101	0x05
8	1000	0x08
10	1010	0x0A
15	1111	0x0F
16	0001 0000	0x10
255	1111 1111	0xFF

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✅ Quick Quiz

1. What is decimal 7 in binary?
2. What is binary 1101 in decimal?
3. What's the maximum value of an 8-bit binary number? (Answer: 255)

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🎉 Summary

What we learned today:

• ✅ Binary only has 0 and 1
• ✅ Can convert using divide-by-2 and weighted sum methods
• ✅ Binary represents switch states and logic values
• ✅ LED arrays can visually demonstrate binary

Next lesson, we'll learn about registers and see how binary is stored in microcontrollers!