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? 64 (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.)
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? 64 (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.)
Chapter8: Sequences, Series,and Probability
Section8.6: Counting Principles
Problem 4ECP: A product’s catalog number is made up of one letter from the English alphabet followed by a...
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Transcribed Image Text: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?
64
(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.)
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