Theory Notes/🗄️ Topic 4: Data & Information Management, Solution Development/10.4.2

10.4.2Grade 10

Number Systems & Character Representation

Everything a computer stores is ultimately just bits — this subtopic is about how those bits represent numbers and characters.

System	Base	Digits used
Decimal	10	0–9 (what humans normally use)
Binary	2	0–1 (what computers natively use)
Hexadecimal	16	0–9 and A–F (a compact way to represent binary)

Converting decimal to binary: repeatedly divide by 2, recording the remainder each time, then read the remainders bottom-to-top.

Example

Convert 13 to binary: 13 ÷ 2 = 6 remainder 1 6 ÷ 2 = 3 remainder 0 3 ÷ 2 = 1 remainder 1 1 ÷ 2 = 0 remainder 1 Reading remainders bottom-to-top: 1101

Converting binary to decimal: multiply each bit by its place value (powers of 2, right to left starting at 2⁰) and sum the results.

Example

Convert 1101 to decimal: (1×8) + (1×4) + (0×2) + (1×1) = 8 + 4 + 0 + 1 = 13

Converting between binary and hexadecimal is fast because each hex digit represents exactly 4 binary bits — group the binary into sets of 4 from the right, then convert each group.

Example

Binary 1101 1010 → group into 4s: 1101 = D, 1010 = A → Hexadecimal: DA

The number of possible combinations for n bits is 2ⁿ. This is why a fixed number of bits limits the range of values you can represent.

Bits	Possible combinations	Unsigned range
4	2⁴ = 16	0–15
8	2⁸ = 256	0–255
16	2¹⁶ = 65 536	0–65 535

Digital character representation — how text is stored as numbers:

ASCII / UTF-8: Character encoding standards that assign a unique number to each character; ASCII covers 128 basic characters (English letters, digits, punctuation) using 7 bits, and UTF-8 extends this to represent virtually any character/language while staying backward-compatible with ASCII.
Unicode: A universal character encoding standard designed to represent characters from every writing system in the world, of which UTF-8 is one common implementation.

💡 Exam Tip

Practise binary/hex/decimal conversions by hand until they're fast and automatic — this is a guaranteed, low-effort-to-master mark source in both papers.