13-bit 2's Complement on .Net MF
To decode the number into decimal, convert it to something your processor understands natively, then use the existing binary to decimal conversion capabilities to convert to decimal.  To convert to native integer representation, all you have to do is sign extend:
II is native signed integer
II &lt;-- 13 bit signed A/D value  (get the A/D result)
II &lt;-- II &amp; 1FFFh               (make really sure limited to 13 bits)
if II >= 1000h                   (negative value ?)
  then II &lt;-- II - 2000h        (convert to native negative)

Note that this is independent of how wide the native signed integer is, as long as it's more than 13 bits.  This means this technique works for both 16 bit and 32 bit signed integers.

Edit: fixed details of sign extending above.  I wrote it right on the scribble paper next to my keyboard, then copied it into the post wrong.  Also added note about it being independent of the native integer size.