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.
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.
-- 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.
n+1 (counting the empty string)
Since there are 8 bits in between, and they can assume any of the two values (0 or 1), that results in a total of 28 different combinations.
Three of them ... the binary numbers 3, 5, and 6. 011 101 110
Every bit can either be a 0 or 1. So to find the amount of bit strings of length either, you do 2length to find the amount of bit strings there are of a given length.
There are (2^5) bit strings of length 5, as each bit can be either 0 or 1. Therefore, the total number of bit strings is (32).
1024
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.
210=1024
Half of them.
There are no zero-length strings that start with 1 bit or end with 2 bits. In a zero-length string, there are no bits at all.
-- 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.
1024 of them.
There are 210.
To find the number of bit strings of length 10 that begin and end with "1", we fix the first and last bits as "1". This leaves us with 8 bits in the middle, which can each be either "0" or "1". Therefore, there are (2^8 = 256) different combinations for the 8 middle bits. Thus, there are 256 bit strings of length 10 that begin and end with "1".
A bit string of length 10 consists of binary digits (0s and 1s). For each of the 10 positions in the string, there are 2 possible choices (either 0 or 1). Therefore, the total number of bit strings of length 10 is (2^{10} = 1024).