Example With n = 7
Here is a more extreme case: with n = 7 the next power of 2 is 8 (we will then use 3 bits or 2 bits if the high bit is discarded) and u = 1:
| Input value |
Offset | Offset value |
Standard Binary |
Truncated Binary |
|---|---|---|---|---|
| 0 | 0 | 0 | 00 | |
| 1 | 1 | 2 | 010 | 010 |
| 2 | 1 | 3 | 011 | 011 |
| 3 | 1 | 4 | 100 | 100 |
| 4 | 1 | 5 | 101 | 101 |
| 5 | 1 | 6 | 110 | 110 |
| 6 | 1 | 7 | 111 | 111 |
This last example demonstrates that a leading zero bit does not always indicate a short code; if u < 2k−1, some long codes will begin with a zero bit.
If n is a power of two, then the encoding may be done with either of two different values of k. Both produce equivalent outputs; one just has u = 2k and encodes all values as "short" k-bit codes, while the other has u = 0 and encodes everything with "long" k+1-bit codes.
Read more about this topic: Truncated Binary Encoding