Number bases represent numbers using different sets of digits. We normally use base 10 (denary), but computers use base 2 (binary).
1. Place value
In binary (base 2) each place is a power of 2: $\dots 8, 4, 2, 1$. So $1010_2 = (1\times 8) + (0\times 4) + (1\times 2) + (0\times 1) = 10$ in base 10.
2. Converting between bases
- To base 10: multiply each digit by its place value and add.
- From base 10: repeatedly divide by the base and read the remainders upwards. So $6 \div 2$ gives remainders that read as $110_2$.
Worked example
Convert $1010_2$ to base 10.
$8 + 0 + 2 + 0 = 10$.
Exam tips
- Binary place values are powers of 2: $1, 2, 4, 8, 16, \dots$
- To convert from base 10, divide repeatedly and read the remainders bottom-to-top.
- The KSSM syllabus covers bases 2, 5 and 8 — the method is the same for each.