Number System
Number Systems (Binary, Decimal, Octal, Hexadecimal and Conversions)
Introduction:
Why Should a Nigerian Student Care About Number Systems?
Think about the last time you used your phone to send a WhatsApp message, watched a YouTube video, or recharged your MTN airtime online. Every single one of those actions happened because a computer somewhere was quietly processing numbers — not the regular 0 to 9 numbers we use every day, but a special kind of number language that machines understand.
Welcome to the world of Number Systems.
If you are in SSS 1 and studying Computer Studies, this is one of the most foundational topics you will ever encounter. Understanding number systems is like learning the alphabet before you start reading — everything else in computing builds on it. From how your JAMB score is stored in a database, to how your bank account balance is kept safe on a server in Lagos, number systems are working silently behind the scenes.
In this lesson, we will break everything down in a way that is simple, clear, and directly connected to things you already know. By the time you finish reading, conversions that once looked scary will feel completely manageable.
Learning Objectives
By the end of this lesson, students should be able to:
- Define the concept of a number system and identify its components
- Explain the four main number systems: binary, decimal, octal, and hexadecimal
- Convert numbers from one system to another using standard methods
- Describe the role of each number system in computer operations
- Demonstrate conversions with worked examples
- Apply knowledge of number systems to solve simple computational problems
What Is a Number System?
A number system is simply a way of representing and expressing quantities using a set of symbols or digits. The total count of unique digits used in a number system is called its base or radix.
For example, in our everyday counting, we use ten digits (0 through 9). That is why our everyday system is called base-10.
Computers, however, do not think the way humans do. They work with electronic circuits that recognise only two states: ON and OFF — represented as 1 and 0. This is why understanding different number systems is so important in computing.
The Four Main Number Systems
1. Decimal Number System (Base 10)
This is the number system every Nigerian child learns from primary school. It uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
The position of each digit determines its value. For example, in the number 345:
- 3 is in the hundreds position (3 × 100 = 300)
- 4 is in the tens position (4 × 10 = 40)
- 5 is in the units position (5 × 1 = 5)
- Total = 345
We use the subscript 10 to show it is decimal — e.g., (345)₁₀
This is the system you use when you count naira notes, calculate your WAEC score, or measure distance from Abuja to Lagos.
2. Binary Number System (Base 2)
The binary system uses only two digits: 0 and 1. It is the native language of computers. Every piece of data in a computer — a photo, a song, a text message — is ultimately stored as a string of 0s and 1s.
Each digit in a binary number is called a bit (short for Binary Digit). A group of 8 bits is called a byte.
Example: (1011)₂
Position values from right to left: 1, 2, 4, 8
So: (1 × 8) + (0 × 4) + (1 × 2) + (1 × 1) = 8 + 0 + 2 + 1 = 11 in decimal
3. Octal Number System (Base 8)
The octal system uses eight digits: 0, 1, 2, 3, 4, 5, 6, and 7. It was more commonly used in older computing systems and still appears in certain programming and file permission settings (especially in Linux/Unix systems).
Example: (47)₈
Position values from right to left: 1, 8
So: (4 × 8) + (7 × 1) = 32 + 7 = 39 in decimal
4. Hexadecimal Number System (Base 16)
The hexadecimal system (often called "hex") uses sixteen symbols: the digits 0–9 and the letters A, B, C, D, E, F.
| Hex | Decimal |
|---|---|
| A | 10 |
| B | 11 |
| C | 12 |
| D | 13 |
| E | 14 |
| F | 15 |
Hexadecimal is widely used in web design (HTML colour codes), computer memory addressing, and programming. Have you ever seen a colour code like #FF5733 on a website or app? That is hexadecimal!
Example: (2F)₁₆
Position values from right to left: 1, 16
So: (2 × 16) + (15 × 1) = 32 + 15 = 47 in decimal
Number System Conversions
This is the part most students find challenging — but with the right method, it becomes straightforward.
Converting Decimal to Binary (Repeated Division by 2)
To convert a decimal number to binary, keep dividing the number by 2 and record the remainders. Read the remainders from bottom to top.
Example: Convert (25)₁₀ to Binary
25 ÷ 2 = 12 remainder 1 12 ÷ 2 = 6 remainder 0 6 ÷ 2 = 3 remainder 0 3 ÷ 2 = 1 remainder 1 1 ÷ 2 = 0 remainder 1
Reading remainders from bottom to top: (11001)₂
Verification: (1×16) + (1×8) + (0×4) + (0×2) + (1×1) = 16 + 8 + 0 + 0 + 1 = 25 ✓
Converting Binary to Decimal (Positional Value Method)
Write down the binary number and assign positional values (powers of 2) from right to left starting at 2⁰.
Example: Convert (110101)₂ to Decimal
Position values: 32, 16, 8, 4, 2, 1
(1×32) + (1×16) + (0×8) + (1×4) + (0×2) + (1×1) = 32 + 16 + 0 + 4 + 0 + 1 = (53)₁₀
Converting Decimal to Octal (Repeated Division by 8)
Divide the decimal number repeatedly by 8 and collect remainders from bottom to top.
Example: Convert (156)₁₀ to Octal
156 ÷ 8 = 19 remainder 4 19 ÷ 8 = 2 remainder 3 2 ÷ 8 = 0 remainder 2
Reading from bottom to top: (234)₈
Converting Decimal to Hexadecimal (Repeated Division by 16)
Divide the decimal number repeatedly by 16 and collect remainders. Replace values 10–15 with A–F.
Example: Convert (255)₁₀ to Hexadecimal
255 ÷ 16 = 15 remainder 15 (F) 15 ÷ 16 = 0 remainder 15 (F)
Reading from bottom to top: (FF)₁₆
This is why the maximum white colour in HTML is #FFFFFF — three pairs of FF representing red, green, and blue at full intensity.
Binary to Hexadecimal Conversion
Group the binary digits in sets of 4 from right to left. Convert each group to its hexadecimal equivalent.
Example: Convert (11011110)₂ to Hexadecimal
Group into 4s: 1101 | 1110
1101 = 13 = D 1110 = 14 = E
Result: (DE)₁₆
Hexadecimal to Binary Conversion
Replace each hex digit with its 4-bit binary equivalent.
Example: Convert (3A)₁₆ to Binary
3 = 0011 A = 1010
Result: (00111010)₂
Summary Table of Number Systems
| Number System | Base | Digits Used | Common Use |
|---|---|---|---|
| Decimal | 10 | 0–9 | Everyday counting and money |
| Binary | 2 | 0, 1 | Computer processing and storage |
| Octal | 8 | 0–7 | Older computing, file systems |
| Hexadecimal | 16 | 0–9, A–F | Web design, memory addressing |
Practical Applications of Number Systems in Nigeria
You might be wondering — when will I ever use this outside of an exam? Here are real situations where these concepts apply:
1. Website Colours: Web designers in Lagos and Abuja use hexadecimal colour codes daily when building websites and mobile apps.
2. Mobile Banking: When you transfer money using your GTBank or Access Bank app, the data is processed by systems that operate in binary internally.
3. Computer Programming: Software developers use hexadecimal codes when debugging programs and working with memory in languages like C++ and Assembly.
4. Network Configuration: IT professionals in Nigeria's telecommunications sector use binary when working with IP addresses (subnetting).
5. File Permissions on Servers: Anyone managing web servers on Linux (common for Nigerian hosting companies) uses octal to set file permissions.
Advantages and Disadvantages of Each Number System
Binary
- Advantage: Simple to implement in hardware; highly reliable
- Disadvantage: Numbers become very long and hard for humans to read
Decimal
- Advantage: Natural and intuitive for humans
- Disadvantage: Not efficient for computer circuits
Octal
- Advantage: Compact representation of binary
- Disadvantage: Not as widely used in modern computing
Hexadecimal
- Advantage: Very compact; easy conversion to/from binary
- Disadvantage: Requires understanding of letters as digits, which can confuse beginners
Digital Safety and Ethical Considerations
As you learn about how computers represent data, it is also important to think about responsibility:
Data Privacy: All your personal information — from your date of birth to your BVN — is stored as binary data on computer systems. This means data security matters. Never share your bank PIN or passwords with anyone, because behind every four-digit PIN is a sequence of 0s and 1s stored in a database.
Accuracy in Computing: Mistakes in binary or hexadecimal coding can lead to serious errors in software — including banking apps, medical devices, and government databases. This is why accuracy in computing is not just academic; it has real-world consequences.
Ethical Use of Technical Knowledge: Understanding how computers store and process data is a privilege. Use it to build, create, and solve problems — not to exploit or manipulate systems unethically.
Classroom and Home Activities
Activity 1 — Conversion Practice Convert the following decimal numbers to binary, octal, and hexadecimal:
- (45)₁₀
- (100)₁₀
- (250)₁₀
Activity 2 — Colour Code Challenge Open any website on your phone or computer and use the browser inspector tool (or a free online colour picker) to find the hexadecimal colour code of three different design elements on the page. Convert each hex code to decimal.
Activity 3 — Binary Counting Race In pairs, students take turns counting from 0 to 15 in binary. The first student to correctly count all 16 values wins.
Activity 4 — Real-Life Research Ask an older sibling, parent, or teacher to explain one way they have encountered binary or hexadecimal in a professional setting. Write a short paragraph about what you learned.
Assessment Questions
Section A — Objective Questions
-
What is the base of the hexadecimal number system? a) 2 b) 8 c) 10 d) 16
-
Convert (1010)₂ to decimal. a) 8 b) 10 c) 12 d) 14
-
Which digits are used in the octal number system? a) 0–9 b) 0–7 c) 0–8 d) 0–15
-
What is the decimal equivalent of (FF)₁₆? a) 225 b) 240 c) 255 d) 256
-
How many bits make up one byte? a) 4 b) 8 c) 16 d) 32
Answers: 1-d, 2-b, 3-b, 4-c, 5-b
Section B — Theory Questions
-
Define a number system and state the base of each of the four number systems studied in this lesson.
-
Convert (237)₁₀ to binary, octal, and hexadecimal, showing all working steps clearly.
-
Explain two practical situations in which the hexadecimal number system is used in computing. Use examples related to the Nigerian technology environment.
Summary
- A number system is a method of representing numbers using a defined set of digits.
- The decimal system (base 10) uses digits 0–9 and is what we use in everyday life.
- The binary system (base 2) uses only 0 and 1 and is the core language of computers.
- The octal system (base 8) uses digits 0–7 and has uses in specific computing environments.
- The hexadecimal system (base 16) uses digits 0–9 and letters A–F, and is widely used in web design, programming, and memory addressing.
- Conversion between these systems follows clear mathematical methods: repeated division for decimal to other bases, and positional value expansion for other bases to decimal.
Conclusion
Number systems may seem abstract at first, but they are the foundation of everything that happens inside a computer. Every song downloaded on Audiomack, every transaction processed by Flutterwave, every post shared on Twitter — all of it ultimately comes down to 0s and 1s moving through electronic circuits at incredible speed.
As a Nigerian student in the digital age, understanding number systems gives you a head start in computer science, software development, cybersecurity, and data management. The world is increasingly run by technology, and the young people who understand how that technology works at its core will be the ones who shape Nigeria's digital future.
Master your conversions. Practice regularly. And remember — every great programmer once sat where you are sitting right now.
Frequently Asked Questions (FAQ)
Q1: Why do computers use binary instead of decimal? Computers are built from electronic switches that have only two states — on (1) and off (0). Binary maps perfectly to these two states, making it the most reliable and efficient system for hardware design.
Q2: Is hexadecimal used in everyday Nigerian life? Yes. Every time a web designer or app developer in Nigeria picks a colour for a website or mobile app, they are using hexadecimal colour codes. It is also used in network configuration and programming.
Q3: How do I remember the hexadecimal letters A to F? Associate them with their decimal values: A=10, B=11, C=12, D=13, E=14, F=15. A simple trick is to remember that after 9 comes the alphabet in sequence — A, B, C, D, E, F.
Q4: Can I use a calculator to do number conversions in exams? For WAEC and NECO, you are generally expected to show manual working. Practise the step-by-step methods until they feel natural. However, calculators or online tools are great for checking your answers at home.
Q5: What is the difference between a bit and a byte? A bit is a single binary digit — either 0 or 1. A byte is a group of 8 bits. All digital storage (kilobytes, megabytes, gigabytes) is measured in units built on bytes.
Q6: Why is octal less commonly taught than binary and hexadecimal? Octal was more relevant in earlier computer architectures. Modern computing systems have largely shifted to hexadecimal because it maps more conveniently to binary (4 bits per hex digit vs 3 bits per octal digit), making it more compact and practical.
This lesson note was written in alignment with the Nigerian NERDC curriculum for SSS 1 Computer Studies. Content is original, educational, and suitable for classroom use and digital publication.
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