GCE A/L ICT Lesson 3: Data Representation and Number Systems

In the digital world, every piece of information—whether it is a text message, a photo, or a video—is stored as a series of numbers. Lesson 3 of the GCE A/L ICT syllabus dives into the mathematical foundation of computing: how data is represented using different number systems.

By using the SchoolICT.net Number System Learning Tool, you can instantly convert between bases and visualize how computers handle complex numerical data.

1. Introduction to Number Systems

Most humans use the Decimal (Base 10) system, but computers operate using the Binary (Base 2) system because electronic circuits have two states: On (1) and Off (0).

Key Number Systems in A/L ICT:

• Binary (Base 2): Uses digits 0 and 1.
• Octal (Base 8): Uses digits 0 to 7.
• Decimal (Base 10): Uses digits 0 to 9.
• Hexadecimal (Base 16): Uses digits 0-9 and letters A-F (where A=10, B=11… F=15).

2. Converting Between Bases

Mastering conversions is essential for scoring in A/L ICT Paper I and II.

From Any Base to Decimal:

Multiply each digit by the base raised to the power of its position.

$$(1101)_2 = (1 \times 2·3) + (1 \times 2·2) + (0 \times 2·1) + (1 \times 2·0) = 8 + 4 + 0 + 1 = 13$$

From Decimal to Any Base:

Repeatedly divide the decimal number by the target base and record the remainders from bottom to top.

Binary to Hexadecimal:

Group binary digits into sets of four (starting from the right) and convert each group directly.

Example: 1011 0101 → B 5 in Hexadecimal.

3. Representing Signed Numbers

Computers must handle negative numbers. There are three primary methods:

1. Sign and Magnitude: The leftmost bit represents the sign (0 for +, 1 for -).
2. One’s Complement: Inverting all bits (0 becomes 1, 1 becomes 0).
3. Two’s Complement: Taking the One’s Complement and adding 1. This is the standard method used in modern computers because it simplifies addition and subtraction.

4. Character Coding Schemes

Since computers only understand numbers, characters (letters and symbols) are assigned specific numerical codes.

• ASCII: 7-bit or 8-bit code representing English characters.
• EBCDIC: Used mainly on IBM mainframe computers.
• Unicode: A universal coding system (16-bit or more) that supports almost every language in the world, including Sinhala and Tamil.

5. Floating Point Representation

To represent very large or very small decimal numbers, computers use Floating Point Representation, which consists of:

• Sign: Is it positive or negative?
• Mantissa: The significant digits of the number.
• Exponent: The power to which the base is raised.

6. Interactive Learning: Number System Tool

Conversions can be tedious and prone to errors. The SchoolICT.net Number System Tool is designed to help you check your work and understand the logic.

Features of the Tool:

• Instant Converter: Type a number in any base (2, 8, 10, or 16) and see the equivalent values in all other bases instantly.
• Two’s Complement Calculator: Enter a negative decimal and watch the tool perform the bit-inversion and addition steps to reach the 8-bit Two’s Complement result.
• Binary Arithmetic Lab: Practice binary addition and subtraction with an automated “Carry” and “Borrow” indicator to help you learn the rules.
• ASCII Lookup: Type a letter and see its corresponding Decimal, Hex, and Binary values.

7. Exam Success Tips for A/L Students

1. Showing Steps: In Paper II, you must show the division or multiplication steps. Don’t just provide the final answer!
2. The Range Rule: Memorize the formula for the range of numbers that can be represented. For $n$ bits in Two’s Complement, the range is:$$-2·{n-1} \text{ to } +(2·{n-1} – 1)$$
3. Hex Shortcut: Always remember that one Hexadecimal digit is exactly 4 Binary bits. This makes converting large numbers much faster.
4. Bit vs. Byte: Be careful with units! Remember that 8 bits = 1 Byte, and prefixes like Kilo (K) in computing usually refer to $2·{10}$ (1024), not 1000.

Conclusion: The Language of the Machine

Lesson 3 is the bridge between human mathematics and computer logic. By mastering data representation, you understand how computers “think” at their most basic level. Use our LMS notes to study the theory and the interactive converter to master your calculations.

Ready to calculate?

• 📖 Read the Full GCE A/L Data Representation Notes
• 💻 Try the Interactive Number System Converter