How many bit strings of length 8 begin and end with a 1?
Keeping this in consideration, how many bit strings of length 8 either start with a 1 or end with a 00?
Number of bit strings of length 8 that start with 1 and end with 00: 25 = 32. Applying the subtraction rule, the number is 128 + 64 − 32 = 160.
Also Know, 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.
Also question is, how many bit strings of length 10 begin and end with a 1?
We are asked about 10 bits, but the first and the last bits are already chosen for us. 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.
How many six bit strings are there that begin with 01?
Similarly, there are 26 bit strings that end with 01. The sum 27+26 double-counts the bit strings that start with 1 and end with 01. There are 25 of these, so there are 27+26−25 bit strings that start with 1 or end with 01.