Hexadecimal and Octal
Base-16 and base-8 representations used in computing.
Key idea
Base-16 and base-8 representations used in computing.
In depth
Hexadecimal (base 16) uses digits 0 to 9 and A to F; octal (base 8) uses 0 to 7. Each hex digit equals exactly four binary digits, making it a compact way to write binary.
Worked example
2F₁₆ = 2×16 + 15 = 47. In binary, 2 = 0010 and F = 1111, so 00101111.
Real-world uses
- Reading memory addresses and colour codes such as #FF8800 in web design
- Unix file permissions
Common mistake
Forgetting that A = 10, B = 11, up to F = 15.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Hexadecimal and Octal?
Base-16 and base-8 representations used in computing. It is a topic at the advanced level in Arithmetic & Number Sense.
Where is Hexadecimal and Octal used in real life?
Real-world examples: Reading memory addresses and colour codes such as #FF8800 in web design; Unix file permissions.
What should I learn before Hexadecimal and Octal?
Make sure you are comfortable with Number Bases, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Hexadecimal and Octal?
Forgetting that A = 10, B = 11, up to F = 15.
How can I practise Hexadecimal and Octal?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Hexadecimal and Octal?
Move on to Roman Numerals next.
Related advanced topics in Arithmetic & Number Sense
- Repeating Decimals – Decimals with a repeating block are rational and convertible to fractions.
- Compound Interest – Interest earned on principal and past interest.
- Inverse Proportion – When one quantity doubles, the other halves.
- Rational Numbers – Numbers expressible as p/q with integers p, q, q≠0.
- Irrational Numbers – Real numbers that cannot be written as a fraction, such as √2 and π.
- Real Numbers – All rational and irrational numbers; the continuous number line.