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How many 8-bit strings do not begin with 10?

a) P(6,2)×P(2,2)
b) 26
c) 28 -C(2,2)
d) 28 - 26

1 Answer

2 votes

Final answer:

There are 256 total 8-bit strings, but only 64 of those start with '10'. Subtracting the latter from the former gives us 192 strings that do not begin with '10'.

Step-by-step explanation:

To answer the question: How many 8-bit strings do not begin with 10?, we need to consider all the 8-bit strings and then subtract those that start with '10'. For an 8-bit string, there are 2 possible values for each bit (0 or 1), leading to a total of 28 possible combinations.

For strings that start with '10', the first two bits are fixed, leaving 6 bits that can vary, leading to 26 such strings. Subtracting the number of strings that start with '10' from the total gives us the answer: 28 - 26.

Converting these powers of 2 gives us 256 (total 8-bit strings) minus 64 (those starting with '10'), which equals 192. The correct choice is (d) 28 - 26, which explains the answer logically and matches the provided choice exactly.

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