Question

1. Two communication devices are using a single-bit even parity check for error detection. The transmitter sends the byte 10101010 and, because of channel noise,

1. the receiver gets the byte 10011010. Will the receiver detect the error? Why or why not?
2. the receiver gets the byte 10111010. Will the receiver detect the error? Why or why not?
3. Compute the Internet checksum for the data block E3 4F 23 96 44 27 99 D3. Then perform the verification calculation.

Answer 1

Solution:

Given,

=>Transmitted byte = 10101010

=>Single bit even parity check for error detection is used.

(a)

Given,

=>Received byte = 1011010

Explanation:

=>The number of 1's in the received byte = 4 which is even and we are using even parity so no error will be detected.

(b)

Given,

=>Received byte = 10111010

Explanation:

=>Number of 1's in the received byte = 5 which is odd and we are using even parity so error will be detected.

(c)

Given,

=>Data block = E3 4F 23 96 44 27 99 D3

Explanation:

Finding checksum:

Step 1:

=>Add the data bytes of all the segments

=>Result = E3 + 4F + 23 + 96 + 44 + 27 + 99 + D3

=>Result = 11100011 + 01001111 + 00100011 + 10010110 + 01000100 + 00100111 + 10011001 + 11010011

=>Result = 1111000010

Step 2:

=>As result contains 10 bits so wrapping around 2 extra bits

=>Result = 11 + 11000010

=>Result = 11000101

Step 3:

=>Taking the 1's complement of result obtained in step 2

=>1's complement of result 11000101 = 00111010

=>Hence checksum = 00111010

=>Checksum in hexadecimal = 3A

Verification:

Step 1:

=>Adding all the data segments and checksum

=>Result = 11100011 + 01001111 + 00100011 + 10010110 + 01000100 + 00100111 + 10011001 + 11010011 + 00111010

=>Result = 1111000010 + 00111010

=>Result = 1111111100

Step 2:

=>Result contains 10 bits so wrapping around 2 extra bits

=>Result = 11111100 + 11

=>Result = 11111111

Step 3:

=>Taking the 1's complement of the result obtained in step 2.

=>1's complement of result = 00000000

=>Hence the checksum has no error and is verified.

I have explained each and every part with the help of statements attached to it.