Solution - Base conversion

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

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

$$14\cdot {16}^2+12\cdot {16}^1+14\cdot {16}^0$$

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

$$3790$$

Expand each digit by place value: $$14·{16}^2$$
+ $$12·{16}^1$$
+ $$14·{16}^0$$. This gives $$3,790$$ in base 10.

$$3790\left(base10\right)$$

Use repeated division by the target base.

$$\frac{3790}{10}$$

Record quotient and remainder for this division cycle.

$$3790=10\cdot 379+0$$

Record quotient and remainder for this division cycle.

$$379=10\cdot 37+9$$

Record quotient and remainder for this division cycle.

$$37=10\cdot 3+7$$

Record quotient and remainder for this division cycle.

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

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

$$3790$$

Final converted representation in the target base.

$${\left(3790\right)}_{10}$$

Repeatedly divide $$3,790$$ by $$10$$, collect remainders, and read them in reverse to get $$3,790$$.