Number Bases

Number base

The number of digits a counting system uses; base ten uses ten digits, base two uses two.

EnglishNumber base
Bahasa MelayuAsas nombor
中文数基

How it is used

To convert 234 in base five to base ten, use place values: 2×5² + 3×5 + 4 = 50 + 15 + 4 = 69. So 234₅ = 69₁₀.

Where it shows up in SPM

This is the core idea of the Number Bases chapter (Form 5). In Paper 1 it appears as quick multiple-choice conversions between base two, five and eight; in Paper 2 you show working when converting a number to base ten or adding two numbers written in the same base.

Don't confuse it with

DigitThe base is how many different digit symbols the system uses; a digit is one of those symbols, so base five uses the five digits 0 to 4.
Place valueThe base fixes the size of each column (powers of the base), while place value is the actual worth a digit gets from the column it sits in.

Open the chapter: Number Bases →

Frequently asked questions

Which bases does SPM actually test?

The KSSM syllabus limits you to base two, base five and base eight, plus base ten. You convert between these and add or subtract numbers within the same base.

You never meet base sixteen or letter digits like A to F in this chapter.

How do I write the base of a number?

Write the base as a small subscript after the number, for example 1011₂ or 47₈. In the exam always show it, because 11 in base two and 11 in base five are completely different values, and a missing subscript can lose you the mark.

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