Explanation:
1 bit = 0 or 1.
8-bit string is a combination of 8 of such bits.
for each position we have 2 possibilities.
that means we have
2×2×2×2×2×2×2×2 = 2⁸ = 256
different possibilities.
how many have at least one 0 ?
only the combination of
11111111
has no 0s.
all others (= 256 - 1 = 255) must therefore have at least one 0.
so,
b) 255 is correct
FYI :
128 would be all possible combinations with 7 bits (2⁷).
127 would mean all combinations of 7 bits with at least one bit being 0.
256 is the total number of different combinations with 8 bits from 00000000 to 11111111.