Binary Numbers
Base-2 system using digits 0 and 1; the language of computers.
Key idea
Base-2 system using digits 0 and 1; the language of computers.
In depth
Binary uses only 0 and 1, with place values 1, 2, 4, 8, ... Computers use it because switches have two states. Convert by summing the powers of 2 that have a 1.
Worked example
1011₂ = 8 + 0 + 2 + 1 = 11. And 13 = 8 + 4 + 1 = 1101₂.
Formula
Real-world uses
- Understanding how computers store data and images
- Reading switch states in digital circuits
Common mistake
Reading binary digits as if they were base ten.
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 Binary Numbers?
Base-2 system using digits 0 and 1; the language of computers. It is a topic at the advanced level in Arithmetic & Number Sense.
What is the formula for Binary Numbers?
The key formula is 1011₂ = 11.
Where is Binary Numbers used in real life?
Real-world examples: Understanding how computers store data and images; Reading switch states in digital circuits.
What should I learn before Binary Numbers?
Make sure you are comfortable with Fractional Exponents, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Binary Numbers?
Reading binary digits as if they were base ten.
How can I practise Binary Numbers?
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 Binary Numbers?
Move on to Number Bases 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.