Encyclopedia > Division by two

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Division by two

Division by two is simple in even-numbered bases.

NOTE: The following methods return only the integer part of the result. No fractions, decimals, or remainders will be returned.

In binary, just shift[?] one place to the right. (Example: 1101001 changes to 110100)

The following algorithm is for decimal. However, it can be used as a model to construct an algorithm for taking half of any number N in any even base.

  • Write out N, putting a zero to its left.
  • Go through the digits of N in overlapping pairs, writing down digits of the result from the following table.

If first digit is EvenEvenEvenEvenEven OddOddOddOddOdd
And second digit is 0 or 12 or 34 or 56 or 78 or 9 0 or 12 or 34 or 56 or 78 or 9
Write 01234 56789

Example: 1738/2=?

Write 01738. We will now work on finding the result.

  • 01: even digit followed by 1, write 0.
  • 17: odd digit followed by 7, write 8.
  • 73: odd digit followed by 3, write 6.
  • 38: odd digit followed by 8, write 9.
Result: 0869.

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