We have the symbols A, B, C, D, E, F, G, H with frequencies 1, 1,...
We have the symbols A, B, C, D, E, F, G, H with frequencies 1,
1, 2, 4, 8, 16, 32, 64.
Show the Huffman tree and Huffman code for the symbols.
How much compression does a 1000 digit file use when using this
Huffman code based on an 8-bit ASCII code (ie, ISO 8859-1)?
Homework Answers
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We have the symbols A, B, C, D, E, F, G, H with frequencies 1,
1,...
An alphabet contains symbols A, B, C, D, E, F. The frequencies of the symbols are...
An alphabet contains symbols A, B, C, D, E, F. The frequencies of the symbols are 35%, 20%, 15%, 15%, 8%, and 7%, respectively. We know that the Huffman algorithm always outputs an optimal prefix code. However, this code is not always unique (obviously we can, e.g., switch 0’s and 1’s and get a different code - but, for some inputs, there are two optimal prefix codes that are more substantially different). For the purposes of this exercise, we consider...
Consider the following symbols with their corresponding frequencies: A:1, B:1, 0:2, D:3, E:5, F:8, G :...
Consider the following symbols with their corresponding frequencies: A:1, B:1, 0:2, D:3, E:5, F:8, G : 13, H: 21 Problem 2.a. (3 points) • Construct the Huffman coding of these symbols along with its optimal coding tree. Problem 2.b. (3 points) • Use your coding tree to decode 0001001000010000000001001
Suppose we have another file with only ASCII symbols. But we decided to encode the file...
Suppose we have another file with only ASCII symbols. But we decided to encode the file in the following way using Huffman Encoding: instead of treating each character as a unique symbol, we use 2 characters together as a unique symbol. For example, if the file content is ABABCCDD. Then there are 4 total symbols (2 ABs, 1 CC, and 1 DD). Please explain how this approach to construct symbols may impact the compression process. More specifically, explain how this...
5. Eight letters {A, B, C, D, E, F,G,H} appear in a 100 letter length message...
5. Eight letters {A, B, C, D, E, F,G,H} appear in a 100 letter length message with the following frequencies: 22, 6, 13, 19, 2, 9, 25, 4. (a) Use Huffman tree to design an optimal binary prefix code for the letters. (b) What is the average bit length of the message after apply codes designed in (a) to the message? [20 marks]
Design the optimal (Huffman) code for the alphabet {a, b, c, d, e, f, g, h,...
Design the optimal (Huffman) code for the alphabet {a, b, c,
d, e, f, g, h, i, j, k, l}, where frequencies are given in the
table below:
Draw the appropriate decoding tree.
a 0.25 g 0.02 b 0.01 h 0.12 c 0.09 i 0.15 d 0.02 j 0.04 e 0.24 k 0.01 f 0.04 l 0.01
Problem (A1) (20 points): Huffman Coding Consider a message having the 5 symbols (A,B,C,D,E) with probabilities...
Problem (A1) (20 points): Huffman Coding Consider a message having the 5 symbols (A,B,C,D,E) with probabilities (0.1,0.1,0.2 ,0.2, 0.4), respectively. For such data, two different sets of Huffman codes can result from a different tie breaking during the construction of the Huffman trees. • Construct the two Huffman trees. (8 points) Construct the Huffman codes for the given symbols for each tree. (4 points) Show that both trees will produce the same average code length. (4 points) For data transmission...
10 marks Question#3 Answer the following Questions 1. How many colors do we have at the...
10 marks Question#3 Answer the following Questions 1. How many colors do we have at the following bit-depth? a. 01 bit = b. 03 bit = C. 04 bit = d. 08 bit = e. 16 bit = 2. In a 4k image, the resolution is 4096 x 2160. a. How many pixels in a 4k image? b. If we divided a 4k image into a block of 8 * 8 pixels. How many blocks we will have? 3. We...
A long string consists of the six characters A, B, C, D, E, F, G; they...
A long string consists of the six characters A, B, C, D, E, F, G; they appear with frequency 21%, 11%, 8%, 17%, 5%, 23%, and 15%, respectively. (a) Draw the Huffman encoding tree of these six characters. (b) What is the Huffman encoding of these six characters? (c) If this encoding is applied to a string consisting of one million characters with the given frequencies, what is the length of the encoded string in bits?
. Huffman Encoding (a.) (6 points) Suppose a certain file contains only the following letters with the corresponding frequencies 1 AİB 73 9 30 44 130 28 16 In a fixed-length encoding scheme, cach...
. Huffman Encoding (a.) (6 points) Suppose a certain file contains only the following letters with the corresponding frequencies 1 AİB 73 9 30 44 130 28 16 In a fixed-length encoding scheme, cach character is given a binary representation with the same number of bits. What is the minimum number of bits required to represent each letter of this file under fixed-length encoding scheme? Describe how to encode all seven letters in this file using the number of bits...
Suppose you have a categorical variable X with nine categories: A, B, C, D, E, F, G, H and I. The frequencies corre...
Suppose you have a categorical variable X with nine categories: A, B, C, D, E, F, G, H and I. The frequencies corresponding to these categories are 25, 12, 7, 4, 6, 2, 1, 0, and 2 Consider now X is a vector of these frequencies and give R expressions that return the categories and its corresponding frequencies as below: X A B D E F G I 25 12 7 4 2 1 0 Now you wish to remove...
Consider the following symbols with their corresponding frequencies: A:1, B:1, 0:2, D:3, E:5, F:8, G : 13, H: 21 Problem 2.a. (3 points) • Construct the Huffman coding of these symbols along with its optimal coding tree. Problem 2.b. (3 points) • Use your coding tree to decode 0001001000010000000001001
5. Eight letters {A, B, C, D, E, F,G,H} appear in a 100 letter length message with the following frequencies: 22, 6, 13, 19, 2, 9, 25, 4. (a) Use Huffman tree to design an optimal binary prefix code for the letters. (b) What is the average bit length of the message after apply codes designed in (a) to the message? [20 marks]
Design the optimal (Huffman) code for the alphabet {a, b, c,
d, e, f, g, h, i, j, k, l}, where frequencies are given in the
table below:
Draw the appropriate decoding tree.
a 0.25 g 0.02 b 0.01 h 0.12 c 0.09 i 0.15 d 0.02 j 0.04 e 0.24 k 0.01 f 0.04 l 0.01
Problem (A1) (20 points): Huffman Coding Consider a message having the 5 symbols (A,B,C,D,E) with probabilities (0.1,0.1,0.2 ,0.2, 0.4), respectively. For such data, two different sets of Huffman codes can result from a different tie breaking during the construction of the Huffman trees. • Construct the two Huffman trees. (8 points) Construct the Huffman codes for the given symbols for each tree. (4 points) Show that both trees will produce the same average code length. (4 points) For data transmission...
10 marks Question#3 Answer the following Questions 1. How many colors do we have at the following bit-depth? a. 01 bit = b. 03 bit = C. 04 bit = d. 08 bit = e. 16 bit = 2. In a 4k image, the resolution is 4096 x 2160. a. How many pixels in a 4k image? b. If we divided a 4k image into a block of 8 * 8 pixels. How many blocks we will have? 3. We...
. Huffman Encoding (a.) (6 points) Suppose a certain file contains only the following letters with the corresponding frequencies 1 AİB 73 9 30 44 130 28 16 In a fixed-length encoding scheme, cach character is given a binary representation with the same number of bits. What is the minimum number of bits required to represent each letter of this file under fixed-length encoding scheme? Describe how to encode all seven letters in this file using the number of bits...
Suppose you have a categorical variable X with nine categories: A, B, C, D, E, F, G, H and I. The frequencies corresponding to these categories are 25, 12, 7, 4, 6, 2, 1, 0, and 2 Consider now X is a vector of these frequencies and give R expressions that return the categories and its corresponding frequencies as below: X A B D E F G I 25 12 7 4 2 1 0 Now you wish to remove...
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