What kind of error is undetectable by the checksum?

Question

What kind of error is undetectable by the checksum?

Answer 1

Suppose that the checksum is the sum of a block of words.  If, in one word, you replace a 0 by a 1, and in another, replace a 1 by a 0 in the same bit position, a checksum will not catch it.

Answer 2

As the name indicate it check the sum of data blocks. So if the errors occur in such a way that sum remain same then it can't predict the error.

e.g I take the example of 4-bits blocks

0000

0001

0010

0000

check sum will be 2'complement of (0011) -> 1101

so the transmitted bits will be

0000

0001

0010

0000

1101

now at receiver, due to presence of noise in channel bit's received are.

0000

0001

0001

0001

1101

receiver will find the sum of first four block.

which is 0011

now he finds 0011 + 1101 = 0000 (Ignoring carry)

so he will assume the data is correct but actually the received data is corrupted.