TAOCP 1.3.1 Exercise 1

A MIX byte must be capable of representing at least $64$ distinct values and at most $100$ distinct values.

taocpmathematicsalgorithmsvolume-1

Section 1.3.1: Description of MIX

Exercise 1. [00] If MIX were a ternary (base 3) computer, how many "trits" would there be per byte?

Verified: yes
Solve time: 3m18s

A MIX byte must be capable of representing at least $64$ distinct values and at most $100$ distinct values. On a ternary computer, a byte containing $t$ trits can represent $3^t$ distinct values. Therefore $t$ must satisfy

$$ 64 \le 3^t \le 100. $$

Since

$$ 3^3=27,\qquad 3^4=81,\qquad 3^5=243, $$

the only power of $3$ lying between $64$ and $100$ is $81=3^4$. Hence a MIX byte on a ternary computer would contain exactly $4$ trits.

$$ \boxed{4\text{ trits per byte}} $$