Exponential-Golomb coding

An exponential-Golomb code (or just Exp-Golomb code) is a type of universal code. To encode any nonnegative integer x using the exp-Golomb code:

1. Write down x+1 in binary
2. Count the bits written, subtract one, and write that number of starting zero bits preceding the previous bit string.

The first few values of the code are:

 0 ⇒ 1 ⇒ 1
 1 ⇒ 10 ⇒ 010
 2 ⇒ 11 ⇒ 011
 3 ⇒ 100 ⇒ 00100
 4 ⇒ 101 ⇒ 00101
 5 ⇒ 110 ⇒ 00110
 6 ⇒ 111 ⇒ 00111
 7 ⇒ 1000 ⇒ 0001000
 8 ⇒ 1001 ⇒ 0001001
...

In the above examples, consider the case 3. For 3, x+1 = 3 + 1 = 4. 4 in binary is '100'. '100' has 3 bits, and 3-1 = 2. Hence add 2 zeros before '100', which is '00100'

Similarly, consider 8. '8 + 1' in binary is '1001'. '1001' has 4 bits, and 4-1 is 3. Hence add 3 zeros before 1001, which is '0001001'.

This is identical to the Elias gamma code of x+1, allowing it to encode 0.