# Division by two

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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 And second digit is Write Even Even Even Even Even Odd Odd Odd Odd Odd 0 or 1 2 or 3 4 or 5 6 or 7 8 or 9 0 or 1 2 or 3 4 or 5 6 or 7 8 or 9 0 1 2 3 4 5 6 7 8 9

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.

From the example we can see that 0 is even.

If the last digit of N is odd digit add .5 to the result.

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