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 | 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.
From the example we can see that 0 is even.
If the last digit of N is odd digit add .5 to the result.