How is 6 trits equal to 9.5 bits?

Question

This reddit thread says 6 trits ~ 9.5 bits.

How is 6 trits ~ 9.5 bits?

Answer 1

Because 3^6 (729) is approximately 2^9.5 (724).

You can read about the ternary number system for more details.

Answer 2

It's talking about information capacity. You can store roughly the same amount of data in 9.5 bits as you can 6 trits because 2^9.5 (724) is approximately 3⁶ (729).

Answer 3

http://en.wikipedia.org/wiki/Ternary_numeral_system

"One trit contains log23 (about 1.58496) bits of information."

1.58496 * 6 ~ 9.5

Answer 4

log(3**6)/log(2) ~ 9.5097750043269382

Answer 5

I suppose, a trit is a "bit with three states" (0, 1 and 2).

Since you can form 3^6=729 different states with 6 trits (every trit can take three different states and you have 6 trits), the above calculation considers how many bits one needs to form 729 different states.

In fact (i.e. reality) you would need ten bits to form 729 different states, but a common calculation to derive how many bits are needed to form a specified number of states is to take the logarithm base 2 of the number. This yields log_2(3^6) = log_2(729) ~ 9.5.

Note: If you want to use the logarithm-base-2 calculation to determine how many bits are needed, you have to take the ceiling of the result.