Error Detection & Correction : MCQs & PYQs with Explanation

Option A

A Checksum is a simple method used in data communication to detect errors in transmitted messages. The basic idea is to sum the numerical values of all data units using one’s complement arithmetic (end-around carry) , and then taking the one’s complement of the final sum. 
End-around carry means add MSB carry-out back into LSB for one’s-complement addition.

• ASCII characters are combined two at a time: the first byte as the high-order byte and the second as the low-order byte of each 16-bit word.
• For "RPSC", ASCII Hex Codes: R = 0x52, P = 0x50, S = 0x53, C = 0x43.
• Form 16-bit words: RP → 0x5250, SC → 0x5343.
• Sum: 0x5250 + 0x5343 = 0xA593; no carry beyond 16 bits, so end-around carry not needed.
• One’s complement: Invert 0xA593 → 0x5A6C. Therefore, the 16-bit checksum is 5A6C.

Option A

A Parity Bit is an extra bit added to binary data during transmission to check whether the data has been transferred correctly or not. It is mainly used for error detection in communication systems. There are two types of parity:

• Even Parity : Total number of 1’s becomes even.
• Odd Parity : Total number of 1’s becomes odd.

Even Parity Example:
Data = 1011001 contains 4 ones, which is already even. Therefore, parity bit 0 is added at the end to keep the total number of ones even. Transmitted data becomes 10110010.
Odd Parity Example:
Data = 1011001 contains 4 ones, which is even. Therefore, parity bit 1 is added at the end to make the total number of one’s odd. Transmitted data becomes 10110011.

Option C

In digital communication and error control coding, the Hamming Distance between two binary codewords is defined as the number of bit positions in which they differ. The minimum Hamming Distance (d) of a code determines its ability to detect and correct errors during data transmission. A larger distance means better error handling capability.
There are two important rules associated with Hamming distance:

• A code with minimum distance d can detect up to (d-1) bit errors.
• A code with minimum distance d can correct up to ⌊(d-1)/2⌋ bit errors.

Here, hamming distance d is given as 5. So, 

• The maximum number of Detectable Errors = 5-1 = 4
• The maximum number of Correctable Errors = ⌊(5-1)/2⌋ = ⌊4/2⌋ = 2

Option A

In networking, multiple access protocols are used to manage how devices share the same communication medium.
In wired networks (Ethernet), devices can easily detect collisions, so CSMA/CD is used. But in wireless networks, devices cannot detect collisions properly because they cannot listen while transmitting. Therefore, CSMA/CA is used in Wi-Fi, and it is not suitable for wired networks.

• CSMA/CD (Carrier Sense Multiple Access with Collision Detection), for wired networks.
• CSMA/CA (Carrier Sense Multiple Access with Collision Avoidance), for wireless networks.

Option A

Automatic Repeat reQuest (ARQ) is a network protocol used to achieve Reliability in data transmission. Its primary function is to ensure that data packets sent from a sender are correctly received by the receiver. If an error is detected in a transmitted packet or if an acknowledgement is not received within a specified timeout period, ARQ triggers the retransmission of that packet until it is correctly received and acknowledged.
This mechanism helps to maintain data integrity and overcome issues such as lost or corrupted packets in unreliable communication channels.

Option C

Stop-and-Wait ARQ is a protocol in which the sender transmits one data packet and waits for an acknowledgement before sending the next packet. Each data packet requires exactly one acknowledgement to confirm its successful receipt. Hence, if 10 data packets are sent, the receiver must send 10 acknowledgements.

Option B

At the Data Link Layer, error detection is used to check whether data has been corrupted during transmission. The most commonly used technique for this purpose is CRC (Cyclic Redundancy Check).
CRC works by treating data as a binary polynomial and dividing it by a predefined generator polynomial. The remainder is attached to the frame and checked at the receiver side.

• Bit Stuffing is used for framing, not error detection.
• Hamming Codes are mainly used for error correction.

Option A

In the Data Link Layer, error control protocols are used to ensure reliable data transmission over an unreliable channel. This is mainly done using ARQ (Automatic Repeat reQuest) techniques.
Types of ARQ Protocols:
Stop-and-Wait ARQ:
In Stop-and-Wait ARQ, the sender sends one frame at a time and waits for an acknowledgement before sending the next. If the ACK is not received, the frame is retransmitted. It is simple but inefficient due to waiting time.
Go-Back-N ARQ:
In Go-Back-N ARQ, the sender sends multiple frames continuously. If an error occurs, it retransmits the erroneous frame and all subsequent frames. It is more efficient than Stop-and-Wait but causes some redundant retransmissions.
Selective Repeat ARQ:
In Selective Repeat ARQ, only the erroneous frames are retransmitted, and the receiver can accept out-of-order frames. It is the most efficient but more complex to implement.
Non-Selective Repeat ARQ is not a standard ARQ protocol. It is just another informal way of referring to Go-Back-N.

Option B

The Hamming Distance is the number of positions at which the corresponding bits of two binary strings are different. To calculate the Hamming distance:

• Both binary numbers must have the same length.
• If their lengths are different, add leading zeros to the shorter binary number.
• Compare the bits one by one and count the number of mismatches.

Given binary numbers are 1101 and 110. First, make both numbers of equal length by adding a leading zero to the shorter number, i.e, 1101 and 0110. Now compare each bit:

Number of different bits are 3. Therefore, Hamming Distance is 3.

Other Examples of Hamming Distance:

Option B

In data communication, error detection and correction are essential for ensuring that transmitted data reaches the destination accurately. Most error control methods can only detect errors, while some can also correct them.
Hamming Code is a special type of code that can both detect and correct single-bit errors. It adds redundant bits called parity bits at specific positions in the data.

Option D

In error control coding, Hamming Distance is the number of bit positions in which two code words differ. It helps in detecting and correcting errors during data transmission.
To correct up to t errors, the code must be able to distinguish between all possible error patterns. For this, the minimum Hamming distance must be sufficiently large.

• To Detect t Errors : Minimum Distance = t+1
• To Correct t Errors : Minimum Distance = 2t+1

Option B

A checksum is used in networking to verify data integrity. It works by adding binary values of data segments and sending the result with the packet. At the receiver’s end, the same calculation is done and compared. If they do not match, an error is detected. However, checksum only supports error detection, not correction.

Option D

Error Detection techniques are used in data communication to identify whether data has been corrupted during transmission. There are several methods used for this purpose.

Option C

Given, 
Message : 1001
CRC Polynomial (CRC Generator) : x³+x+1, binary 1011 (Degree 3)
Append 3 zero to the message because degree of polynomial is 3 or n-1 times (if n is CRC Generator).
Now perform Binary Division (Modulo 2):
Divide 1001000 by 1011 (Binary Division, XOR for Subtraction)
1001000 ÷ 1011, Remainder is 110.
This remainder is CRC bit.
Transmitted Message : Original Message + CRC Bits = 1001 + 110 = 1001110

Option D

Error correction uses Hamming distance, which counts the number of differing bits between two words.
Received word: 01000

The received word is at equal minimum distance (1) from codeword A and codeword C. Since two valid codewords are equally close, the receiver cannot uniquely determine the correct codeword.
Therefore, the system cannot correct the error.