A bit string is a finite sequence of $0$’s and $1$’s. How many bit
strings of length $8$ begin and end with a $1$?
My answer would be: $2^6$. 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 $2^6 = 64$.
Is this the correct answer?
Best Answer
Yes the answer $2^6$ is correct. Two bits you know are $1$ already, so there are $8-2=6$ bits left. Each bit can either be a $0$ or a $1$, so you have $2$ possibilities for each slot. Hence, as you concluded correctly, you have $2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 = 2^6$ possible combinations for your string.