Lesson 21: Conversion From Any Base to Base 10

What is Conversion?

Conversion is the act of changing a number from one number system to another. To convert from base 2, base 8, or base 16 to base 10, rank the digits from right to left starting with zero, then express the number using its base.

Base 2 to Base 10

(1011)₂ = 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8+0+2+1 = (11)₁₀

(101.011)₂ = 1×2² + 0×2¹ + 1×2⁰ + 0×2^-1 + 1×2^-2 + 1×2^-3 = 4+0+1+0+0.25+0.125 = (5.375)₁₀

Base 8 to Base 10

(237)₈ = 2×8² + 3×8¹ + 7×8⁰ = 128+24+7 = (159)₁₀

Base 16 to Base 10

(4AC9)₁₆ = 4×16³ + 10×16² + 12×16¹ + 9×16⁰ = (19145)₁₀