3. The following 11-bit Hamming-coded (single-bit correction) string was receive
ID: 3621781 • Letter: 3
Question
3. The following 11-bit Hamming-coded (single-bit correction) string was received. Which bit is in error, if any?10101101110
4. Construct an 11-bit Hamming code for the characters C and Z.
5. Calculate the cyclic checksum remainder using the longhand division method and the hardware shift method for the message 11001100. Use the following polynomial checksum: x7 + x4 + x2 + 1.
6. Given the following message:
This is a good class
Show the arithmetic checksum (in hex) that is generated from this message. Show all work.
1. Perform run-length compression on the binary string 1000110000000000000001000000010000
2. What are the three steps used in JPEG compression?
3. What is the Hamming Distance for the 7-bit ASCII character set? How can you increase this Hamming Distance by 1?
4. Given the generating polynomial x6 + x3 + x2 +1 and the data 10101111, show the remainder created using longhand division.
5. Given the message “This is fun”, show the arithmetic checksum that will be generated (don’t include the quotation marks, and don’t forget the blanks). (For the exam, I will provide an ASCII chart if necessary.)
6. In SONET, what does the Section Overhead control? Path Overhead? Line Overhead? What is the duration of a SONET frame? Looking at SONET’s Synchronous Payload Envelope, how much user data is included in each frame?
7. What is the maximum number of channels in a T-1 frame? How much overhead is inserted in each T-1 frame? What is this overhead used for? What is meant by the term “bit robbing” or “bit stealing”?
8. What is the function of a label edge router in an MPLS-enabled network?
9. Show the sequence of PPP frames that are sent (protocol and code fields only) when a device tries to connect to a network and CHAP is used for authentication. Also include the PPP frames sent when the connection is finished.
10. What are the different types (“sizes”) of fiber optic cable?
11. What frequency signal do you need if you want to transmit at 56,000 bps with a signal to noise ratio of 80 to 1?
12. How many signal levels are necessary to transmit a 20,000 bps using a 5000 Hz signal?
13. Show the constellation pattern for a modulation technique that uses 16 phase levels.
14. Be able to create a Huffman code given four symbols, A, G, C and T, where their percentages of occurrence are 14%, 36%, 40%, and 10% respectively.
15. Given the ASCII character 1001010, show the 11-bit forward error correction code that will be generated.
Explanation / Answer
4. Given data word with parity bits is 10101101110. As, the parity bits are located at all powers-of-two bit positions, the parity bits in the given code word are P1 – 0, p2 – 1, p3 – 1, p4 – 0 We now, verify the parity bit values using even parity. Parity bit 1 P1 (1) contributes to 3, 5,7,9,11 bit positions. So, by counting the parity of these bit positions we get p1as 0. So we can say that no error occurred in parity bit 1 Similarly, P2 (2) contributes – 3, 6, 7,10,11 So, p2 = 0 and has occurred error P3 (4) - 5,6,7; p3 = 0, error occurred P4(8)- 9,10,11; p4 = 0, no error Now we evaluate the value of the parity bits from left to right as P4 p3 p2 p1 – 0 0 1 0 The decimal value of 0010 is 2. So it specifies that the 2nd bit in the data word has changed and it is to be flipped. 5. C – 1000011, Z – 1011010 Hamming code for C: If the bits of a codeword are numbered from 1 to n,parity bits are located at all power-of-two bit positions, with the data bits interspersed in the remaining bit positions. So it is represented as, 1 0 0 _0 0 1 _ 1 _ _ Blanks represent the parity bit position where they are to be inserted. Parity bit 1 P1 contributes to 1, 3, 5,7,9,11,13 bit positions. It counts the parity of these bit positions. P2 (2) – 2,3,6,7,10,11,14 P3 (4)- 4,5,6,7,12,13,14 P4(8)- 8,9,10,11,12,13,14 Considering the even parity, we get the P1 = 1, p2=0, p3=1,p4=1. Now by inserting these parity values in the blank spaces, we get the required code word Hence the code word for the given word is 10010011101 For Z: It is represented as 1 0 1 – 1 0 1 – 0 - - we get the P1 = 0, p2=0, p3=0,p4=0 by inserting these parity values in the blank spaces, we get the required code word Hence the code word for the given word is 10101010000 Only one question is to be posted per one post
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