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	Even	Even	Even	Even	Even	Odd	Odd	Odd	Odd	Odd
And second digit is	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
Write	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.