Question

Calculate the traditional checksum for the byte sequence in hex: 31, 20, 2D, 41, 4A by adding all bytes and etc... If received byte sequence is 31, 20, 2D, 4A, 41 and received a checksum, can the checksum detect the error? Can the CRC-10 above detect the error?

Answer 1

Given :

Traditional checksum for the byte sequence in hex: 31, 20,2D,41,4A can be calculated by adding all bytes and etc.

The received byte sequence is 31,20,2D,4A,41 and received a checksum.

Solution:

First of all converting hex to binary,

we will get,

00110001

00100000

00101101

01000001

01001010

add all the segments of bits:

00110001 + 00100000 + 00101101 + 01000001 + 01001010 = 100001001 (9 bits)

since the result contains 1 extra bit so we need to wrap around an extra bit to convert into 8 bits.

00001001 + 01 = 00001010

Now take the 1's complement of the above result and we will get the traditional checksum,

1's complement of 00001010 = 11110101

at the receiver side:

00110001

00100000

00101101

01001010

01000001

along the bytes of data, we also get checksum as 11110101

add all the segments :

00110001 + 00100000   + 00101101 + 01001010 + 01000001 = 100001001 (9 bits)

9 bits so we need to wrap around extra 1 bit,

00001001 + 01 = 00001010

Now take the 1's complement of the above result

1's complement of 00001010 = 11110101 which is equal to traditional checksum so checksum can't detect this error

CRC is used to detect a single-bit error but here many bits are flipped in data at the receiver side as compared to the sender side so CRC-10 can't detect this error.