How many bit strings of length eight either start with a 1 bit or end with the two bits 00?
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Also to know is, how many bit strings of length ten either start with a 1 bit or end with the two bits 00?
Bits are either 1 or 0, so there are 2 choices per bit, and 8 bits to choose. Therefore, there are 28 = 256 bit strings of length ten that begin and end with a 1.
Similarly, how many bit strings of length 8 or less are there? There are 28 which is 256. That means there are 256 different values you can store in a byte, since a byte is eight bits. There are 256 eight-bit ascii codes, for instance.
Considering this, how many bit strings of length 8 begin and end with a 1?
My answer would be: 26. Because we know, that the bit starts with 1 and ends with 1: Which means, that 2 of the length 8 is used, also there are 6 positions remaining, which is 26=64.
How many 8 bit strings have at least two consecutive 0's or two consecutive 1's?
There are only two 8-bit strings in which the bits alternate: 10101010 and 01010101. The total number of 8-bit strings with no restrictions is 2^8. Therefore the number of 8-bit strings which have at least two consecutive 0's or at least two consecutive 1's is 2^8 - 2.