Question

Given the coding scheme a: 001, b: 0001, e: 1, r: 0000,s: 0100, t: 011, x: 01010, find the word represented by,

a) 01110100011.

b) 0001110000.

c) 0100101010.

d) 01100101010.

Short answer

1. Test
2. Beer
3. Sex
4. Tax

Step-by-step solution

One needs to find words of the first prefix codes,

The first prefix code is 01110100011.

We can decode this as:

\(\begin{array}{l}{\bf{011}}\,\,\,\,{\bf{1}}\,\,\,\,{\bf{0100}}\,\,\,\,{\bf{011}}\\\,\,\,{\bf{t}}\,\,\,\,\,\,\,{\bf{e}}\,\,\,\,\,\,\,\,{\bf{s}}\,\,\,\,\,\,\,\,\,\,\,\,{\bf{t}}\end{array}\)

Therefore, the first word is test.

 Step 2: One needs to find words of the second prefix codes,

The second prefix code is 0001110000.

One can decode this as:

\(\begin{array}{l}{\bf{0001}}\,\,\,\,{\bf{1}}\,\,\,\,{\bf{1}}\,\,\,\,{\bf{0000}}\\\,\,\,\,\,{\bf{b}}\,\,\,\,\,\,\,{\bf{e}}\,\,\,{\bf{e}}\,\,\,\,\,\,\,\,{\bf{r}}\end{array}\)

Therefore, the word is beer.

One needs to find words of the third prefix codes,

The third prefix code is 0100101010.

One can decode this as:

\(\begin{array}{l}{\bf{0100}}\,\,\,\,{\bf{1}}\,\,\,\,{\bf{01010}}\\\,\,\,\,{\bf{s}}\,\,\,\,\,\,\,\,\,{\bf{e}}\,\,\,\,\,\,\,\,\,{\bf{x}}\end{array}\)

Therefore, the word is sex.

One needs to find words of the fourth prefix codes,

The fourth code is 01100101010.

One can decode this as:

\(\begin{array}{l}{\bf{011}}\,\,\,\,\,{\bf{001}}\,\,\,\,{\bf{01010}}\\\,\,\,\,{\bf{t}}\,\,\,\,\,\,\,\,\,\,{\bf{a}}\,\,\,\,\,\,\,\,\,\,\,\,\,{\bf{x}}\end{array}\)

Therefore, the word is tax.