capable of being written or set down in writing.
Computers. capable of recording data: writable DVDs.
Also, writeable.

unwritable, adjective
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
write (raɪt)
vb , writes, writing, wrote, written
1.  to draw or mark (symbols, words, etc) on a surface, usually paper, with a pen, pencil, or other instrument
2.  to describe or record (ideas, experiences, etc) in writing
3.  to compose (a letter) to or correspond regularly with (a person, organization, etc)
4.  (tr; may take a clause as object) to say or communicate by letter: he wrote that he was on his way
5.  informal chiefly (US), (Canadian) (tr) to send a letter to (a person, etc)
6.  to write (words) in cursive as opposed to printed style
7.  (tr) to be sufficiently familiar with (a specified style, language, etc) to use it in writing
8.  to be the author or composer of (books, music, etc)
9.  (tr) to fill in the details for (a document, form, etc)
10.  (tr) to draw up or draft
11.  (tr) to produce by writing: he wrote ten pages
12.  (tr) to show clearly: envy was written all over his face
13.  (tr) to spell, inscribe, or entitle
14.  (tr) to ordain or prophesy: it is written
15.  (tr) to sit (an examination)
16.  (intr) to produce writing as specified
17.  computing Compare read to record (data) in a location in a storage device
18.  (tr) Compare underwrite
[Old English wrītan (originally: to scratch runes into bark); related to Old Frisian wrīta, Old Norse rīta, Old High German rīzan (German reissen to tear)]

Collins English Dictionary - Complete & Unabridged 10th Edition
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Example sentences
It is also working on ways to make its holographic discs re-writable.
The ability of media to be used repeatedly, ie to be re-writable, is also an important requirement.
The file may be read only, access to the file may be restricted, or the disk may be full or non-writable.
Code was added at all places where writing to disk is possible, to specify the path of a writable disk and directory.
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