Solution - Base conversion

$${\left(4F5\right)}_{16}$$

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

$$4\cdot {16}^2+15\cdot {16}^1+5\cdot {16}^0$$

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

$$1269$$

Expand each digit by place value: $$4·{16}^2$$
+ $$15·{16}^1$$
+ $$5·{16}^0$$. This gives $$1,269$$ in base 10.

$$1269\left(base10\right)$$

Use repeated division by the target base.

$$\frac{1269}{10}$$

Record quotient and remainder for this division cycle.

$$1269=10\cdot 126+9$$

Record quotient and remainder for this division cycle.

$$126=10\cdot 12+6$$

Record quotient and remainder for this division cycle.

$$12=10\cdot 1+2$$

Record quotient and remainder for this division cycle.

$$1=10\cdot 0+1$$

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

$$1269$$

Final converted representation in the target base.

$${\left(1269\right)}_{10}$$

Repeatedly divide $$1,269$$ by $$10$$, collect remainders, and read them in reverse to get $$1,269$$.