cs601 assignment 3 solution fall 2019 2020

cs601 assignment 3 solution fall 2019 2020
Question No. 1
Suppose a message consisting of following four-bit numbers is being sent to a destination. By writing all necessary calculation steps, you are required to calculate four-bit Checksum number, the sender will append with the original message:
9, 8,11, 15, 14
Solution:
Sum of the numbers= 9+8+11+15+14=57
(9, 8, 11, 15, 14) is the message appended with the checksum where 57 is the sum of original numbers.
Here the = 9+8+11+15+14 are 4-bits because each number is less than 15
The number57 cannot be written in 4-bits
The number 57 is equal to (111001)2 which is also greater than 4-bits
To change it to 4-bits number we add extra left most bit to the right four bits as shown below
Left bits=(11)2 , right four bits=(1001)2
(1110)2=14 which is 4-bits
Question No. 2
Considering the Generator Polynomial (Divisor): X3+1, by writing all necessary calculations steps involved in Cyclic Redundancy Check, you are required to determine the codeword of the following data word:
10110
Solution:
Polynomial=X3+1, the degree of polynomial is three
The divisor will be X3+1=1001
Question No. 3
Find the Polynomials equivalent of bits given in the following table:
Bits | Polynomial |
1010000 | X7+X5+0 |
10001001 | X8+X4+1 |
1010000 | X7+X5+0 |
10001001 | X8+X4+1 |