A bit is a 0 or a 1. A bit string of length 8 is a sequence of 8 digits, all of which are either 0 and 1.

(a) How many bit strings of length 8 are there?

(b) How many bit strings of length 8 or less are there?

a) N = 2^8 = 256

b) N = 2^8 + 2^7 + 2^6 + 2^5 + 2^4 + 2^3 + 2^2 + 2^1

Step-by-step explanation:

Given;

String of length 8, with two options (0 or 1) each.

a) for the number of bits of strings of length 8.

Each digit of the 8 digit string has 2 options.

For 8 digit, we have

N = 2*2*2 ... = 2^8 = 256

b) for bit of strings of length 8 or less.

For n string = 2^n

For n < 8

The number of bit strings for length 8 or less are;

N = N8 + N7 + N6 + ... + N1

N = 2^8 + 2^7 + 2^6 + 2^5 + 2^4 + 2^3 + 2^2 + 2^1