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How many 8-bit strings are there that have at least one zero? a) 256 b) 255 c) 128 d) 127

User Bummzack
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1 Answer

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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.

User Oddmeter
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