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Base System

Base System​

Place value:

(abc)_b = a*b^2 + b_digit*b + c

Decimal to base b:

  1. Repeatedly divide by b.
  2. Record remainders.
  3. Read remainders bottom to top.

Base b to decimal:

Multiply each digit by powers of b and add.

Speed checks:

  • In base b, allowed digits are 0 to b-1.
  • Last digit determines divisibility by base factors.