1.1 Compare and contrast notational systems
📘CompTIA ITF+ (FC0-U61)
What Is Decimal Notation?
Decimal notation is the standard number system that humans use every day.
It is also called the base-10 system because it uses 10 digits:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
In IT, decimal numbers appear in many places such as:
- IP addresses (e.g., 192.168.1.10)
- File sizes shown to users (e.g., 500 MB, 2 GB)
- CPU clock speeds (e.g., 3.4 GHz)
- Storage capacity (e.g., 256 GB SSD)
- Decimal security codes or error codes
For the CompTIA ITF+ exam, you must understand what decimal is, how it compares to other notational systems, and how it is used in computing.
Key Characteristics of Decimal (Base-10)
✔ Digits Used
Decimal uses 10 possible digits (0–9).
After 9, the system rolls over to another place value (like 10, 11, 12…).
✔ Place Values
Each place value increases by powers of 10:
| Place Value | Meaning |
|---|---|
| 10⁰ | Ones |
| 10¹ | Tens |
| 10² | Hundreds |
| 10³ | Thousands |
Example:
In the number 348,
- 3 represents 300 (3 × 10²)
- 4 represents 40 (4 × 10¹)
- 8 represents 8 (8 × 10⁰)
This positional structure is a core idea in all numbering systems (binary, hex, etc.).
Why Decimal Is Important in IT
Even though computers use binary, humans continue to use decimal for easier reading and understanding.
Here’s where you see decimal numbers in IT:
1. IP Addressing (IPv4)
IPv4 addresses are written in four decimal numbers, each ranging from 0 to 255.
Example:192.168.0.15
Even though the computer interprets it in binary, humans read and manage IPs in decimal format because it is easier to understand.
2. System Storage and File Sizes
When users see storage capacity or file sizes, they typically see decimal values:
- 500 GB HDD
- 128 GB USB drive
- 5 MB document
While the underlying system may calculate using binary, the final display often uses decimal-based prefixes (kilo, mega, giga).
3. Performance Metrics
Decimal numbers show performance values in IT:
- CPU clock speed → 3.5 GHz
- Network speed → 100 Mbps, 1 Gbps
- Power consumption → 65 W
All these are represented using regular base-10 decimal numbers.
4. Software and Application Settings
Applications often use decimal values for:
- Screen resolution: 1920 × 1080
- Zoom levels: 100%, 125%, 150%
- Color codes in decimal: RGB values (0–255)
These values are shown in decimal because they are easier for humans to read.
Comparing Decimal to Other Notation Systems
For the exam, you must compare decimal with binary, hexadecimal, and octal.
Here is a simple comparison:
| System | Base | Digits Used | Common Use in IT |
|---|---|---|---|
| Decimal | 10 | 0–9 | User-facing values (IP, sizes, settings) |
| Binary | 2 | 0–1 | Machine language, memory, CPU operations |
| Hexadecimal | 16 | 0–9, A–F | Memory addresses, color codes |
| Octal | 8 | 0–7 | Legacy systems, Unix permissions |
Important for the exam:
Decimal is the standard human-friendly representation, while computers operate internally in binary.
Decimal Conversions (Basic Awareness)
The ITF+ exam may ask simple questions about comparing decimal to other notational systems.
You do not need to perform long conversions, but you must understand the concepts.
Binary → Decimal
Binary represents powers of 2.
Example:1010 in binary:
- 1 × 2³ = 8
- 0 × 2² = 0
- 1 × 2¹ = 2
- 0 × 2⁰ = 0
Total = 10 (decimal)
Hexadecimal → Decimal
Hex uses powers of 16.
Example:1A in hex:
- 1 × 16 = 16
- A = 10 → 10 × 1 = 10
Total = 26 (decimal)
This level of understanding is enough for ITF+.
Decimal in Operating Systems & Networking
1. System Logs
Error codes may appear in decimal:
- Error code: 404
- Event ID: 1001
- Status: 200 OK
2. Port Numbers
Ports are decimal values:
- HTTP → 80
- HTTPS → 443
- DNS → 53
3. Permissions & Access Control
Some systems show quantity limits using decimal, e.g.:
- Maximum login attempts: 5
- Password length requirements: 8–12 characters
Exam Tips for Decimal Notation
✔ You must know that decimal is base 10.
✔ You should be able to compare decimal to binary, octal, and hexadecimal.
✔ You should understand where decimal is used in IT.
✔ Memorize the digits 0–9 only.
✔ Understand that decimal is mostly for human readability.
✔ Know that computers do not process decimal internally — they convert it to binary.
Short Summary (Useful for Revision)
- Decimal = Base 10
- Digits = 0–9
- Used by humans, not computers internally
- Found in IP addresses, file sizes, port numbers, system settings, logs, and metrics
- Important for comparing to binary (base 2), octal (base 8), and hex (base 16)
