Number system question

Question

Is it true that if we are given a number system with base 3, mantissa 2, $-1 \le p \le 1$, determined by $$\pm 0.d_1 d_2 \times 3^p$$ where each number is normalized, unless it is zero, then the smallest positive number would be $0.10 \times 3^{-1}$, and the biggest would be $0.22 \times 3^1$? Just want to make sure I'm not mistaken in my understanding of the concept. Some feedback would be appreciated.

Answer 1

Think of all the numbers arranged on a number line with numbers to the right of zero deemed positive and numbers to the left of zero as negative.

The value of a number is said to be where it appears on the number line. The number furthest to the right (if there is one) is the number with maximum value and the number furthest to the left (again, if there is one) is the number with minimum value. If every number has a value (it appears somewhere on our number line) then we can order them from smallest to largest.

The magnitude of a number is how far away it is from 0. The number(s) closest to zero have the smallest magnitude and the number(s) furthest away have the largest magnitude.

For example, on the real number line $-3$ has a smaller value than $2$ (it is to the left of $2$), but $-3$ has a greater magnitude that $2$ (as it is further from $0$ than $2$ is). Meanwhile $-1$ has a smaller value than $1$, but they have the same magnitude.