**Error Detection and Correction**.

#### Begin and Good luck!

**Choose the letter of the best answer in each questions.**

1. Checksums use _________ arithmetic.

A) one’s complement arithmetic

B) two’s complement arithmetic

C) either (a) or (b)

D) none of the above

Answer: **Option A**

Solution:

2. The checksum of 1111 and 1111 is _________.

A) 0000

B) 1111

C) 1110

D) 0111

Answer: **Option A**

Solution:

3. In modulo-11 arithmetic, we use only the integers in the range ______, inclusive.

A) 1 to 10

B) 0 to 10

C) 1 to 11

D) none of the above

Answer: **Option B**

Solution:

4. In cyclic redundancy checking, the divisor is _______ the CRC.

A) one bit less than

B) one bit more than

C) The same size as

D) none of the above

Answer: **Option B**

Solution:

5. The ________ between two words is the number of differences between corresponding bits.

A) Hamming rule

B) Hamming code

C) Hamming distance

D) none of the above

Answer: **Option C**

Solution:

6. The _______ of a polynomial is the highest power in the polynomial.

A) range

B) power

C) degree

D) none of the above

Answer: **Option C**

Solution:

7. In modulo-2 arithmetic, __________ give the same results.

A) addition and subtraction

B) addition and multiplication

C) addition and division

D) none of the above

Answer: **Option A**

Solution:

8. In cyclic redundancy checking, what is the CRC?

A) The quotient

B) The dividend

C) The divisor

D) The remainder

Answer: **Option D**

Solution:

9. Which error detection method consists of just one redundant bit per data unit?

A) CRC

B) Checksum

C) Simple parity check

D) Two-dimensional parity check

Answer: **Option C**

Solution:

10. In _____ coding, we divide our message into blocks, each of k bits, called ___.

A) block; blockwords

B) block; datawords

C) linear; datawords

D) none of the above

Answer: **Option B**

Solution:

11. A _____ error means that two or more bits in the data unit have changed.

A) burst

B) double-bit

C) single-bit

D) none of the above

Answer: **Option A**

Solution:

12. Adding 1 and 1 in modulo-2 arithmetic results in _________.

A) 0

B) 1

C) 2

D) none of the above

Answer: **Option A**

Solution:

13. In ________ error correction, the receiver corrects errors without requesting retransmission.

A) onward

B) forward

C) backward

D) none of the above

Answer: **Option B**

Solution:

14. If the Hamming distance between a dataword and the corresponding codeword is three, there are _____ bits in error.

A) 5

B) 4

C) 3

D) none of the above

Answer: **Option C**

Solution:

15. A simple parity-check code can detect __________ errors.

A) an odd-number of

B) an even-number of

C) two

D) no errors

Answer: **Option A**

Solution:

16. The Hamming distance between equal codewords is _________.

A) 0

B) 1

C) n

D) none of the above

Answer: **Option A**

Solution:

17. In a linear block code, the _______ of any two valid codewords creates another valid codeword.

A) ANDing

B) XORing

C) ORing

D) none of the above

Answer: **Option B**

Solution:

18. In ________ error correction, the receiver asks the sender to send the data again.

A) forward

B) backward

C) retransmission

D) none of the above

Answer: **Option C**

Solution:

19. We can divide coding schemes into two broad categories: ________ and ______coding.

A) linear; nonlinear

B) block; convolution

C) block; linear

D) none of the above

Answer: **Option B**

Solution:

20. In modulo-2 arithmetic, we use only ______.

A) 1 and 2

B) 0 and 1

C) 0 and 2

D) none of the above

Answer: **Option B**

Solution:

21. To guarantee correction of up to 5 errors in all cases, the minimum Hamming distance in a block code must be ________.

A) 11

B) 6

C) 5

D) none of the above

Answer: **Option A**

Solution:

22. The _____of errors is more difficult than the ______.

A) detection; correction

B) correction; detection

C) creation; correction

D) creation; detection

Answer: **Option B**

Solution:

23. In block coding, if k = 2 and n = 3, we have _______ invalid codewords.

A) 4

B) 8

C) 2

D) none of the above

Answer: **Option A**

Solution:

24. The checksum of 0000 and 0000 is __________.

A) 0000

B) 1111

C) 0111

D) 1110

Answer: **Option B**

Solution:

25. In one’s complement arithmetic, if positive 7 is 0111, then negative 7 is ________.

A) 1101

B) 1000

C) 1111

D) none of the above

Answer: **Option B**

Solution:

26. In block coding, if n = 5, the maximum Hamming distance between two codewords is ________.

A) 5

B) 3

C) 2

D) none of the above

Answer: **Option A**

Solution:

27. Which error detection method uses one’s complement arithmetic?

A) Checksum

B) CRC

C) Simple parity check

D) Two-dimensional parity check

Answer: **Option A**

Solution:

28. The divisor in a cyclic code is normally called the _________.

A) redundancy

B) degree

C) generator

D) none of the above

Answer: **Option C**

Solution:

29. In modulo-2 arithmetic, we use the ______ operation for both addition and subtraction.

A) OR

B) XOR

C) AND

D) none of the above

Answer: **Option B**

Solution:

30. We add r redundant bits to each block to make the length n = k + r. The resulting n-bit blocks are called _________.

A) codewords

B) datawords

C) blockwords

D) none of the above

Answer: **Option A**

Solution:

31. To guarantee the detection of up to 5 errors in all cases, the minimum Hamming distance in a block code must be _______.

A) 11

B) 5

C) 6

D) none of the above

Answer: **Option C**

Solution:

32. A generator that contains a factor of ____ can detect all odd-numbered errors.

A) x

B) 1

C) x + 1

D) none of the above

Answer: **Option C**

Solution:

33. _______codes are special linear block codes with one extra property. If a codeword is rotated, the result is another codeword.

A) Convolution

B) Cyclic

C) Non-linear

D) none of the above

Answer: **Option B**

Solution:

34. The Hamming distance between 100 and 001 is ________.

A) 0

B) 1

C) 2

D) none of the above

Answer: **Option C**

Solution:

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