Number Bases

This topic covers how numbers are written in different bases. You will learn place value in bases other than 10, how to convert between base 10 and other bases, and how to add and subtract in base 2, base 5 and base 8.

  • Place value in other bases
  • Base 10 to base n and back
  • Addition and subtraction in base 2, 5, 8

Lessons for Number Bases

Place Value and Base Systems

What is a base?The base tells us how many different digits are used and what each position is worth.In base …

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Converting Base 10 to Another Base

Method: Repeated divisionDivide by the new base and record the remainder. Read remainders upwards.Example: 2510 to base 225 ÷ 2 …

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Addition in Base 2, 5 and 8

RuleAdd like normal, but when the sum reaches the base, carry 1.Base 21+1 = 102 (write 0 carry 1).Example: 10112 …

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Subtraction in Base 2, 5 and 8

RuleSubtract like normal. If the top digit is too small, borrow 1 = the base.Base 20 - 1 needs a …

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Exercises for Number Bases

Write the value in base 10

Convert to base 10:101121101224354053781268

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Convert from base 10

Convert:1310 to base 21910 to base 25810 to base 512110 to base 54510 to base 810010 to base 8

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Add in bases

Work out (do not convert to base 10):11012 + 10121112 + 1121435 + 325445 + 235258 + 468778 + 68

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Subtract in bases

Work out (do not convert to base 10):11002 - 101210002 - 122315 - 4451005 - 25638 - 2781008 - 18

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