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Toolkit 104

Number Base Representations and Conversions

Number Representation in Base b

0≤ai≤b−10\le a_i\le b-1

Base 3 to 10

(2102)3=2⋅33+1⋅32+0⋅3+2=65(2102)_3=2\cdot3^3+1\cdot3^2+0\cdot3+2=65

Base b to 10

(anan−1⋯a1a0)b=a0+a1b+a2b2+⋯+anbn(a_na_{n-1}\cdots a_1a_0)_b=a_0+a_1b+a_2b^2+\cdots+a_nb^n

Base 10 to 3

Decimal to base conversion using remainders
65=(2102)365=(2102)_3

Repeated division gives the digits from the remainders.

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