A bit is either a 0 or a 1. A byte is a sequence of 8 bits and a nibble is a sequence of 4 bits. a) How many different nibbles are possible? Write out the sample space. b) What is the probability that a randomly generated nibble has two adjacent 1’s?

a) 16 possible nibbles , sample space: {0000, 0001, 0010, 0011, 0100, 0101, 0110, 0111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111}

b) 1/2

Explanation:

a) A nibble is composed of 4 bits and each bit can get two values (1 or 0). Therefore total number of  possible configurations can be calculated as

N=2^4=16

Sample space can be written as below,

{0000, 0001, 0010, 0011, 0100, 0101, 0110, 0111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111}

b) By checking the sample space there are 8 different combinations {0011, 0110, 0111, 1011, 1100, 1101, 1110, 1111} that has two adjacent 1's over 16 possible combinations. Therefore the possibility is 8/16=1/2.