1. The problem is to find the value of $2$ divided by $\frac{1}{2}$. 2. The formula for dividing by a fraction is to multiply by its reciprocal. That is, $a \div \frac{b}{c} = a \times \frac{c}{b}$. 3. Applying this rule, we have: $$2 \div \frac{1}{2} = 2 \times \frac{2}{1}$$ 4. Multiply the numbers: $$2 \times 2 = 4$$ 5. Therefore, the answer is $4$.