Find the number of terms and the sum of the geometric progression 8, 4, 2, ..., 1/512.

The first term is $a = 8$.
The common ratio is $r = \frac{4}{8} = \frac{1}{2}$.
The last term is $l = \frac{1}{512}$.

The formula for the $n$-th term of a geometric progression is $l = a \cdot r^{n-1}$.
Substitute the known values:

Divide both sides by 8:

Since $2^{12} = 4096$, we can write:

Equating the exponents:

There are 13 terms in the progression.

The formula for the sum of the first $n$ terms of a geometric progression is $S_n = \frac{a(1 - r^n)}{1 - r}$ (since $|r| < 1$).
Substitute $a=8$, $r=\frac{1}{2}$, and $n=13$:

Calculate $\left(\frac{1}{2}\right)^{13}$:

Substitute this back into the sum formula:

Rounding 15.998046875 to the nearest whole number gives 16.

The sum of the progression, rounded to the nearest whole number, is $\boxed{16}$.