1. **State the problem:** We need to calculate $2$ divided by $64$. 2. **Write the division as a fraction:** $$\frac{2}{64}$$ 3. **Simplify the fraction:** Both numerator and denominator can be divided by $2$. $$\frac{\cancel{2}}{\cancel{64}} = \frac{1}{32}$$ 4. **Final answer:** $$\frac{1}{32}$$ This means $2$ divided by $64$ equals $\frac{1}{32}$.