A bit string is a finite sequence of 0s and 1s How many bit

A bit string is a finite sequence of 0\'s and 1\'s. How many bit strings have length 8? How many bit strings of length 8 begin with three 0\'s? What is the probability a bit string of length 8 begins and ends with a 1?

Solution

a)

In a string of length 8 each bit can be either 0 or 1

So, 2^8=256 strings

b)

So we are fixiding the first three bits to 0s

Now 5 bits left to allocated with 1s or 0s

So, 2^5 strings

c)

Fixing the first and last bit with 1 leaves 6 bits to be allocated with 1s or 0s so 2^6 strings

So probablity is :2^6/2^8=1/4