Solution - Base conversion

$${\left(FF\right)}_{16}$$

Expand digits with place-value powers in the source base.

$$15\cdot {16}^1+15\cdot {16}^0$$

Sum the expanded terms to obtain the base-10 value.

$$255$$

Expand each digit by place value: $$15·{16}^1$$
+ $$15·{16}^0$$. This gives $$255$$ in base 10.

$$255\left(base10\right)$$

Use repeated division by the target base.

$$\frac{255}{10}$$

Record quotient and remainder for this division cycle.

$$255=10\cdot 25+5$$

Record quotient and remainder for this division cycle.

$$25=10\cdot 2+5$$

Record quotient and remainder for this division cycle.

$$2=10\cdot 0+2$$

Read remainders from last to first to form target-base digits.

$$255$$

Final converted representation in the target base.

$${\left(255\right)}_{10}$$

Repeatedly divide $$255$$ by $$10$$, collect remainders, and read them in reverse to get $$255$$.