1.1 Compare and contrast notational systems

📘CompTIA ITF+ (FC0-U61)

1.1 Notational Systems – Hexadecimal (Base-16)

CompTIA ITF+ Exam Explanation (Easy and IT-Focused)

Hexadecimal—often called hex—is a numbering system based on 16 values. It is widely used in computing because it makes binary data shorter, easier to read, and easier for humans to work with.

What Is Hexadecimal?

Hexadecimal is a base-16 numbering system.
This means it uses 16 symbols:

0 1 2 3 4 5 6 7 8 9 A B C D E F

0–9 work the same as in decimal (base-10).
A–F represent values 10–15.

Hex	Decimal
A	10
B	11
C	12
D	13
E	14
F	15

Why base-16?
Because computers work in binary (base-2), and hexadecimal maps very neatly to binary, making long binary numbers shorter and more human-friendly.

Why Hexadecimal Matters in IT

Hexadecimal appears in many places in IT. On the exam, you must know where and why it’s used.

✔ 1. Memory Addresses (RAM and CPU registers)

Operating systems and hardware often represent memory locations in hexadecimal because:

Memory addresses are large binary numbers.
Hex is a readable way to represent them.

Example:
0x7FFE34A0 (memory address)
(“0x” means “this is hex.”)

✔ 2. MAC Addresses

A MAC address (network card address) uses 12 hexadecimal characters.

Example:
A4-5E-60-B2-3F-19

Why hex here?

Each pair of hex digits equals 8 bits (1 byte).
Network devices can process them quickly.

✔ 3. IP Version 6 (IPv6) Addresses

IPv6 uses hexadecimal to make large addresses easier to work with.

Example:
2001:0db8:85a3:0000:0000:8a2e:0370:7334

Without hex, IPv6 would be hundreds of binary digits.

✔ 4. File Permissions, Error Codes, and Debugging

Developers and technicians often see hex values in:

system logs
error messages
debug output
crash reports
memory dumps

Example:
Error Code: 0x80070005

Hex allows precise identification of issues.

✔ 5. Color Codes in Digital Design (HTML/CSS)

Web colors are represented using hexadecimal values.

Example:
#FF0000 (red)

Each pair (FF, 00, 00) represents RGB values in hex.

This is often tested at a basic awareness level.

How Hexadecimal Works (Simple Explanation)

Hexadecimal is structured like other numbering systems but with base-16.

Place Values in Hex (powers of 16)

Place	Value
16²	256
16¹	16
16⁰	1

Example hex number:
3A

Convert to decimal:

3 × 16 = 48
A = 10 × 1 = 10
Total = 58 decimal

You do not have to perform heavy conversions on the ITF+ exam, but you should understand the concept.

Binary and Hexadecimal Relationship (Important for Exam)

Each hex digit = 4 bits.

Hex	Binary
0	0000
1	0001
2	0010
3	0011
4	0100
5	0101
6	0110
7	0111
8	1000
9	1001
A	1010
B	1011
C	1100
D	1101
E	1110
F	1111

This direct mapping is the main reason computers use hex.

Quick Hex Conversions (Useful for Exam)

Hex → Decimal (simple method)

Example: 2F

2 × 16 = 32
F = 15
Result = 47

Hex → Binary (digit-by-digit)

Example: 9A

9 = 1001
A = 1010

Binary = 10011010

Binary → Hex (group in 4 bits)

Binary: 1101 0110

1101 = D
0110 = 6

Hex = D6

The ITF+ exam focuses more on recognition and purpose, not deep math.

Where You Will See Hexadecimal on the ITF+ Exam

Expect questions such as:

✔ What base does hexadecimal use?
✔ What digits are included in hexadecimal?
✔ Why do IT professionals use hex instead of binary?
✔ Which IT components use hex?
✔ Identify a hexadecimal value.
✔ Convert a simple hex number to decimal or binary.
✔ Pick out which values are valid hex numbers.

Common Exam-Level Key Points to Remember

Hexadecimal = base-16.
Uses digits 0–9 and A–F.
Converts easily to binary (each hex digit = 4 bits).
Used in IPv6 addresses, MAC addresses, memory addresses, color codes, error messages, etc.
Hex numbers often start with 0x, #, or appear in groups like FF or A4.
Hex makes long binary numbers shorter and readable.

Summary

Hexadecimal is a base-16 numbering system used throughout computing because:

It is compact.
It is easier for humans to read than binary.
It maps cleanly to binary.
It appears in many IT environments such as networking, memory, troubleshooting, and web development.

Understanding these basics is enough to fully answer any hexadecimal-based question on the CompTIA ITF+ exam.