Number System SS1 Digital Technologies Lesson Note

Subject: Digital Technologies 

Class: SS1

How Humans vs. Computers Count

In our daily lives, we use the Decimal System. Why? Because we have ten fingers! We count from 0 to 9, and once we hit 10, we start combining numbers.

However, computers don’t have fingers. They have “switches” that are either ON or OFF. Because of this, they use a different system.

The Four Main Systems we will learn:

1. Decimal (Base 10): What we use (0, 1, 2, 3, 4, 5, 6, 7, 8, 9).
2. Binary (Base 2): What computers use (0, 1).
3. Octal (Base 8): Used to shorten long binary strings (0, 1, 2, 3, 4, 5, 6, 7).
4. Hexadecimal (Base 16): Used for colors and memory addresses (0-9 and A-F).

Binary—The Language of 1s and 0s

The word Binary comes from “Bi” (like a bicycle with two wheels). It only uses two digits: 0 and 1.

• 0 means “Off” or “False.”
• 1 means “On” or “True.”

Every photo you take, every song you play, and every text you send is actually just a very long string of 1s and 0s.

Wait, what about Hexadecimal? When numbers get too long in binary (like 101101101), humans find it hard to read. Hexadecimal (Base 16) is like a “shorthand” to make those numbers shorter. It uses 0–9, then switches to letters:

• A = 10, B = 11, C = 12, D = 13, E = 14, F = 15.

Converting Decimal to Binary (The “Divide by 2” Method)

To turn a normal number (Decimal) into a computer number (Binary), we use a simple “Remainders” method.

Example: Convert 13 to Binary

1. 13 ÷ 2 = 6 (Remainder 1)
2. 6 ÷ 2 = 3 (Remainder 0)
3. 3 ÷ 2 = 1 (Remainder 1)
4. 1 ÷ 2 = 0 (Remainder 1)

Now, read the remainders from the bottom to the top: The answer is 1101.

Note: Always write the base as a small number at the bottom so we know which system it is.

1310​=11012​

Converting Binary back to Decimal

If your computer gives you the binary code 1011, how do you know what it means in human language? We use Place Values (Powers of 2).

Example: Convert 1011 to Decimal We write the powers of 2 above the numbers from right to left:

• 23=8 | 22=4 | 21=2 | 20=1
• 1 | 0 | 1 | 1

Now, add up only the numbers where there is a “1”: (1×8)+(0×4)+(1×2)+(1×1) 8+0+2+1=11.

So, 10112​ is actually 11 in our normal counting!

Summary and Comparison Table

To wrap up, here is a quick “Cheat Sheet” for how these numbers look.

Why does this matter? As an IT student, knowing this helps you understand how data is stored. If you ever become a programmer or a hardware engineer, you’ll see these “Hex” codes when fixing computer errors or designing websites!

Class Work

1. Why do computers use Binary instead of Decimal?
2. Convert the number 25 from Decimal to Binary.
3. What does the letter “C” represent in Hexadecimal?
4. Convert 1110 from Binary to Decimal.