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 10 we use digits 0-9. 235₁₀ = 2×10² + 3×10¹ + 5×10⁰.

Other bases

Base 2 (binary): digits 0,1 only. 1011₂ = 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8+0+2+1 = 11₁₀.

Base 5: digits 0-4. 234₅ = 2×5² + 3×5¹ + 4×5⁰ = 50+15+4 = 69₁₀.

Base 8 (octal): digits 0-7. 17₈ = 1×8¹ + 7×8⁰ = 8+7 = 15₁₀.

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