An approach I've used: count the number of leading 1 bits, say n. The size of the number is then 2^n bytes (including the leading 1 bits). Take the bits after the first 0 bit as an integer, and add the maximum value (plus one) that can be represented by a number using this encoding in 2^(n-1) bytes.

Thus,

0b00000000 -> 0
0b01111111 -> 127
0b10000000 00000000 -> 128
0b10000000 00000001 -> 129
0b10111111 11111111 -> 16511
0b11000000 00000000 00000000 00000000 -> 16512
0b11011111 11111111 11111111 11111111 -> 536887423

etc.

This scheme allows any non-negative value to be represented in exactly one way.

(Equivalently, used the number of leading 0 bits.)

An approach I've used: count the number of leading 1 bits, say n. The size of the number is then 2^n bytes (including the leading 1 bits). Take the bits after the first 0 bit as an integer, and add the maximum value (plus one) that can be represented by a number using this encoding in 2^(n-1) bytes.

Thus,

                  0 = 0b00000000
                   ...
                127 = 0b01111111
                128 = 0b1000000000000000
                   ...
              16511 = 0b1011111111111111
              16512 = 0b11000000000000000000000000000000
                   ...
          536887423 = 0b11011111111111111111111111111111
          536887424 = 0b1110000000000000000000000000000000000000000000000000000000000000
                   ...
1152921505143734399 = 0b1110111111111111111111111111111111111111111111111111111111111111
1152921505143734400 = 0b111100000000000000000000000000000000000000000000 ...

This scheme allows any non-negative value to be represented in exactly one way.

(Equivalently, used the number of leading 0 bits.)

An approach I've used: count the number of leading 0 bits, say n. The size of the number is then 2^n bytes (including the leading 0 bits). Take the bits after the first 1 bit as an integer, and add the maximum value (plus one) that can be represented by a number using this encoding in 2^(n-1) bytes.

Thus, 0b10000000 -> 0, 0b11111111 -> 127, 0b01000000 00000000 -> 128, etc.

This scheme allows any non-negative value to be represented in exactly one way.

An approach I've used: count the number of leading 1 bits, say n. The size of the number is then 2^n bytes (including the leading 1 bits). Take the bits after the first 0 bit as an integer, and add the maximum value (plus one) that can be represented by a number using this encoding in 2^(n-1) bytes.

Thus,

0b00000000 -> 0
0b01111111 -> 127
0b10000000 00000000 -> 128
0b10000000 00000001 -> 129
0b10111111 11111111 -> 16511
0b11000000 00000000 00000000 00000000 -> 16512
0b11011111 11111111 11111111 11111111 -> 536887423

etc.

This scheme allows any non-negative value to be represented in exactly one way.

(Equivalently, used the number of leading 0 bits.)