Solution - Base conversion

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

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

$$12\cdot {16}^2+13\cdot {16}^1+12\cdot {16}^0$$

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

$$3292$$

Expand each digit by place value: $$12·{16}^2$$
+ $$13·{16}^1$$
+ $$12·{16}^0$$. This gives $$3,292$$ in base 10.

$$3292\left(base10\right)$$

Use repeated division by the target base.

$$\frac{3292}{10}$$

Record quotient and remainder for this division cycle.

$$3292=10\cdot 329+2$$

Record quotient and remainder for this division cycle.

$$329=10\cdot 32+9$$

Record quotient and remainder for this division cycle.

$$32=10\cdot 3+2$$

Record quotient and remainder for this division cycle.

$$3=10\cdot 0+3$$

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

$$3292$$

Final converted representation in the target base.

$${\left(3292\right)}_{10}$$

Repeatedly divide $$3,292$$ by $$10$$, collect remainders, and read them in reverse to get $$3,292$$.