Solution - Base conversion

$${\left(5C9\right)}_{16}$$

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

$$5\cdot {16}^2+12\cdot {16}^1+9\cdot {16}^0$$

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

$$1481$$

Expand each digit by place value: $$5·{16}^2$$
+ $$12·{16}^1$$
+ $$9·{16}^0$$. This gives $$1,481$$ in base 10.

$$1481\left(base10\right)$$

Use repeated division by the target base.

$$\frac{1481}{10}$$

Record quotient and remainder for this division cycle.

$$1481=10\cdot 148+1$$

Record quotient and remainder for this division cycle.

$$148=10\cdot 14+8$$

Record quotient and remainder for this division cycle.

$$14=10\cdot 1+4$$

Record quotient and remainder for this division cycle.

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

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

$$1481$$

Final converted representation in the target base.

$${\left(1481\right)}_{10}$$

Repeatedly divide $$1,481$$ by $$10$$, collect remainders, and read them in reverse to get $$1,481$$.