Grade 10 · Theory
Number systems
Data representation, storage and social implications · about 4 min
Reading a binary number by adding its place values.1 MIN READ
2 study sections · pause after each one and recall the key ideaComputers work in binary (base 2) because circuits have two reliable states: on and off. Programmers also use hexadecimal (base 16) as a compact way to write binary.
Key points- Decimal (base 10) uses digits 0–9; binary (base 2) uses only 0 and 1; hexadecimal (base 16) uses 0–9 and A–F.
- Converting binary → decimal: add the place values (128, 64, 32, 16, 8, 4, 2, 1) where a 1 appears.
- Converting decimal → binary: repeatedly subtract the largest power of two (or divide by 2 and track remainders).
- One hex digit represents exactly four binary bits, so hex is a shorthand for binary.
- Example: 1101₂ = 8+4+1 = 13₁₀ = D₁₆.
- Bit — a single binary digit (0 or 1).
- Byte — 8 bits; the basic unit of storage.
EXAM TIP
show your working in conversions — method marks are awarded even if the final answer slips.