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Number Bases · Form 4

Number Bases: Worked Examples (Easier)

One-step number base practice: converting a number from base 2, 5 or 8 into base ten using place value. Best for students who are meeting number bases for the first time.

Written by the spmmath.com.my editorial team.

Worked example 1

Convert 1101₂ to base ten.

  1. Write the place values from the right: 2³, 2², 2¹, 2⁰ = 8, 4, 2, 1.
  2. Multiply each digit by its place value: (1×8) + (1×4) + (0×2) + (1×1).
  3. Compute: 8 + 4 + 0 + 1 = 13.

Worked example 2

Convert 324₅ to base ten.

  1. Write the place values from the right: 5², 5¹, 5⁰ = 25, 5, 1.
  2. Multiply each digit by its place value: (3×25) + (2×5) + (4×1).
  3. Compute: 75 + 10 + 4 = 89.

Worked example 3

Convert 57₈ to base ten.

  1. Write the place values from the right: 8¹, 8⁰ = 8, 1.
  2. Multiply each digit by its place value: (5×8) + (7×1).
  3. Compute: 40 + 7 = 47.

Worked example 4

Convert 11010₂ to base ten.

  1. Write the place values from the right: 2⁴, 2³, 2², 2¹, 2⁰ = 16, 8, 4, 2, 1.
  2. Multiply each digit by its place value: 1×16 + 1×8 + 0×4 + 1×2 + 0×1.
  3. Add: 16 + 8 + 0 + 2 + 0 = 26.

Worked example 5

Convert 243₅ to base ten.

  1. Write the place values from the right: 5², 5¹, 5⁰ = 25, 5, 1.
  2. Multiply each digit by its place value: 2×25 + 4×5 + 3×1.
  3. Add: 50 + 20 + 3 = 73.

Worked example 6

Convert 165₈ to base ten.

  1. Write the place values from the right: 8², 8¹, 8⁰ = 64, 8, 1.
  2. Multiply each digit by its place value: 1×64 + 6×8 + 5×1.
  3. Add: 64 + 48 + 5 = 117.

Worked example 7

Convert 1001₂ to base ten.

  1. 1001₂ = (1×2³) + (0×2²) + (0×2¹) + (1×2⁰)
  2. = 8 + 0 + 0 + 1

Worked example 8

Convert 246₈ to base ten.

  1. 246₈ = (2×8²) + (4×8¹) + (6×8⁰)
  2. = (2×64) + (4×8) + 6
  3. = 128 + 32 + 6

Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)

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Frequently asked questions

What's the quickest way to convert a number to base ten?

Multiply each digit by its place value (a power of the base, starting from the rightmost digit as power 0) and add the results together. For example, in base two each place value doubles moving left, getting these place-value powers right is the main skill being tested.

How do I convert a base ten number into another base?

Repeatedly divide the number by the target base and record each remainder, then read the remainders from bottom to top. A common mistake is reading them top to bottom or losing track of a remainder of zero, so keep your division steps organised in a column.

Why do I keep making mistakes converting between base two and base eight?

These conversions usually go through base ten as a middle step unless you're using a direct grouping method. Rushing and mixing up digit order is the main cause of errors, write out the place values clearly and double-check by converting your answer back.

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