Counting in other bases

Binary, base 4 and beyond: how the same number looks different in another base. About 9 minutes, GCSE / A-level.

What you will do

  1. We count in tens. In base 10, each place is worth ten times the one to its right: 1, 10, 100... In base 2 (binary), each place is worth two times the one on its right: 1, 2, 4, 8... and the only digits are 0 and 1.
  2. Convert 255 to binary. Divide by 2 again and again and keep the remainders, then read them from the bottom up.
  3. Back to ordinary numbers. To go the other way, add up each digit times its place value.
  4. Fractions in another base. For the part after the point, multiply by the base again and again and keep the whole-number parts.
  5. Your turn. Convert it.

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