TBE

Truncated Binary Encoding

https://en.wikipedia.org/wiki/Truncated_binary_encoding

k = floor_log2(n);
u = 2 * exp2(k) - n

Writing

if x < u write k least significant bits of x else add u to x and write k most significant bits of x and then write a least significant bit of x.

Reading

1. read k bits as x.
2. if u <= x then read an additional bit and add it to x as a least significant bit and substract u.

Examples (MSB first)

n = 2

k = 1;
u = 4 - 2 = 2;

n = 3

k = 2;
u = 1

n = 4

k = 2
u = 8 - 4 = 4

n = 5

k = 2;
u = 3;

n = 6

k = 2;
u = 2;

n = 7

n = 10

k = 3;
u = 6;