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How many bit strings are there of length six or less not counting the empty string?
That's just the highest number that can be counted with 6 bits ... 127 .
How many different bit strings are there of length 7?
The number of different bit strings of length 7 can be calculated using the formula 2^n, where n is the length of the bit string. In this case, with a length of 7, there are 2^7 = 128 different bit strings possible. This is because each bit in the string can have 2 possible values (0 or 1), and there are 7 bits in total.
How many bit strings of length 8 are there which begin with a 0 and end with a 0?
-- There are 256 bit strings of length 8 . -- There are 4 bit strings of length 2, and you've restricted 2 of the 8 bits to 1 of those 4 . -- So you've restricted the whole byte to 1/4 of its possible values = 64 of them.
In a bit string length 12 How many begin with 110?
You are essentially asking how many different bit strings of length 9 are there, as the first 3 bits are fixed. The answer is 2^9 = 512.
How many bit strings of length not exceeding n consist entirely of 1s?
n+1 (counting the empty string)
