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: