Let A be the set of all strings of O's and 1's, and let T be the set of all strings of O's and 1's that consist of consecutive triples of identical bits. Consider the coding and decoding functions E and D defined in Example 7.1.9. The encoding function E: A → T is defined as follows. For each string s E A, E(s) = the string obtained from s by replacing each bit of s by the same bit written three times. The decoding function D: T → A is defined as follows. For each string t e T, D(t) = the string obtained from t by replacing each consecutive triple of three identical bits of t by a single copy of that bit. (a) Find E (0110) and D (111111000111). E (0110) D (111111000111) (b) Find E (1010) and D (000000111111). E (1010) D (000000111111)

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Chapter2: Second-order Linear Odes
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Let A be the set of all strings of 0's and 1's, and let T be the set of all strings of 0's and 1's that consist of consecutive triples of identical bits. Consider the coding and decoding functions E and D defined in Example 7.1.9.

The encoding function EA → T is defined as follows. For each string s ∈ AE(s) = the string obtained from s by replacing each bit of s by the same bit written three times.

The decoding function DT → A is defined as follows. For each string t ∈ TD(t) = the string obtained from t by replacing each consecutive triple of three identical bits of t by a single copy of that bit.

(a) Find E (0110) and D (111111000111).

(b) Find E (1010) and D (000000111111).

Let A be the set of all strings of 0's and 1's, and let T be the set of all strings of O's and 1's that consist of consecutive triples of identical bits. Consider the coding and
decoding functions E and D defined in Example 7.1.9.
The encoding function E: A → T is defined as follows. For each string s E A, E(s) = the string obtained from s by replacing each bit of s by the same bit written
%3D
three times.
The decoding function D: T → A is defined as follows. For each string t E T, D(t) = the string obtained from t by replacing each consecutive triple of three
identical bits of t by a single copy of that bit.
(a) Find E (0110) and D (111111000111).
E (0110)
%3D
D (111111000111)
(b)
Find E (1010) and D (000000111111).
Е (1010)
D (000000111111)
%3D
Transcribed Image Text:Let A be the set of all strings of 0's and 1's, and let T be the set of all strings of O's and 1's that consist of consecutive triples of identical bits. Consider the coding and decoding functions E and D defined in Example 7.1.9. The encoding function E: A → T is defined as follows. For each string s E A, E(s) = the string obtained from s by replacing each bit of s by the same bit written %3D three times. The decoding function D: T → A is defined as follows. For each string t E T, D(t) = the string obtained from t by replacing each consecutive triple of three identical bits of t by a single copy of that bit. (a) Find E (0110) and D (111111000111). E (0110) %3D D (111111000111) (b) Find E (1010) and D (000000111111). Е (1010) D (000000111111) %3D
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