A four-bit code word is any sequence of four digits, where each digit is either

Question

A four-bit code word is any sequence of four digits, where each digit is either a 0 or a 1. For example, 0100 and 1011 are four-bit code words. Complete parts (a) through (d) below (a) How many different four-bit code words are there? 16 (b) How many different six-bit code words, such as 001011, are there? (c) if a vocabulary of 1000 code words is required, how long must the words be? At least 10 bits (d) What is the probability that a randomly selected four-bit code word has no 0 following any 1? (Type an integer or a simplified fraction)

Explanation / Answer

a) as for each digit we have 2 options (0 or 1) therefore total number of four bit code =2*2*2*2=16

b)

total number of six bit code =2*2*2*2*2*2=64

c)for 512 <1000<1024

29 <1000 <210

therefore at least 10 bit lenthy word needs to be there

d)total number of 4 digit word =16

possible number of 4 digit word with no 0 following any 1 ={ 0000; 0001; 0011 ; 0111 ; 1111} =5

hence required probability =favourable outcome/total outcome =5/16

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