Data compression：練習問題

Why is data compression frequently used when storing or transmitting files over a network?

A short text document takes up \(700\) bits of space when stored using \(7\)-bit ASCII. After applying Huffman coding, the file size is reduced to \(380\) bits. How many bits have been saved through compression?

In a Huffman tree, the following character codes are assigned:
- 'E' is represented by \(0\)
- 'T' is represented by \(10\)
- 'A' is represented by \(11\)

What is the binary representation of the word 'TEA' using these codes?

A row of pixels in a black and white bitmap is represented by the binary string: 0000111000000. Which of the following represents this data using Run Length Encoding (RLE) frequency/data pairs?

Explain one reason why it is often necessary or desirable to use data compression when storing files on a computer.

Use Run Length Encoding (RLE) to represent the following binary data as frequency/data pairs:
00000011100000

A message contains the characters 'AAAAABCC'. Calculate the total bits required using 7-bit ASCII and determine how many bits are saved if Huffman coding is used with the following codes: A=0, B=10, C=11.

Run Length Encoding (RLE) is a form of lossless data compression.
Part A: Explain the purpose of data compression in computer systems.
Part B: A row of pixels in a simple bitmap is represented by the following binary string:
000000111111110000
Represent this data using RLE frequency/data pairs as specified in the syllabus.

The following Huffman tree is used to encode a message containing the characters A, B, C, and D.
- The path to A is 0
- The path to B is 10
- The path to C is 110
- The path to D is 111

Part A: Decode the following bitstream using the tree: 110010111.
Part B: Calculate how many bits would be required to store the string "ABACAD" using this Huffman tree.
Part C: Calculate the number of bits required to store the same string "ABACAD" using standard 7-bit ASCII.