Number Bases
Binary (base two)
A number system using only the digits 0 and 1.
| English | Binary (base two) |
|---|---|
| Bahasa Melayu | Perduaan (asas dua) |
| 中文 | 二进制（基数二） |
How it is used
To convert 1011 base two to base ten, add the place values of the 1s: 1×8 + 0×4 + 1×2 + 1×1 = 8 + 2 + 1 = 11. So 1011₂ = 11₁₀.
Where it shows up in SPM
Binary is the most-tested base in the Number Bases chapter (Form 5). Paper 1 asks you to convert between binary and base ten or eight; Paper 2 often asks you to add or subtract two binary numbers, where you carry a 1 whenever a column reaches two.
Don't confuse it with
Open the chapter: Number Bases →
Frequently asked questions
How do I add two binary numbers?
Add column by column from the right: 0+0=0, 0+1=1, and 1+1=10, so you write 0 and carry 1. For example 101₂ + 11₂: rightmost 1+1=10 (write 0 carry 1), then 0+1+1=10 (write 0 carry 1), then 1+0+1=10, giving 1000₂.
What is the quickest way to convert base ten to binary?
Divide by two repeatedly and record the remainders. For 13: 13÷2=6 r1, 6÷2=3 r0, 3÷2=1 r1, 1÷2=0 r1.
Read the remainders from the bottom up to get 1101₂.