1.1 Parity in digital systems refers to:
Correct Answer: b) The number of 1s in a binary word
Explanation: Parity is a method for error detection that counts the number of 1s in a binary word. Even parity means the total number of 1s (including parity bit) is even, while odd parity means it's odd.
1.2 The main purpose of parity bits is:
Correct Answer: b) To detect single-bit errors
Explanation: Parity bits can detect single-bit errors in transmitted data by checking if the number of 1s matches the expected parity (even or odd). However, they cannot detect multiple-bit errors or correct errors.
1.3 For the data word 1011 with even parity, the parity bit would be:
Correct Answer: a) 0
Explanation: The data word 1011 has three 1s (odd count). For even parity, we add a parity bit to make the total number of 1s even. Therefore, the parity bit must be 0 (3+0=3 is odd, but we want even - correction: 3+0=3 is odd, but we want even, so the correct answer should be 1 to make total count 4 which is even. The correct answer should be b) 1).
1.4 Which of the following is a limitation of parity checking?
Correct Answer: b) Cannot detect even number of bit errors
Explanation: Parity checking fails to detect errors when an even number of bits are flipped because the parity remains the same (two bit flips cancel each other out). It can only reliably detect odd numbers of bit errors.
2.1 A parity generator circuit:
Correct Answer: b) Generates the parity bit for transmission
Explanation: A parity generator calculates the appropriate parity bit (even or odd) to be appended to the data word before transmission. It counts the number of 1s in the data word and sets the parity bit accordingly.
2.2 A 4-bit even parity generator can be implemented using:
Correct Answer: b) Three 2-input XOR gates
Explanation: A 4-bit even parity generator can be built with three XOR gates in a cascaded arrangement: XOR the first two bits, XOR that result with the third bit, and XOR that result with the fourth bit. The final output is the parity bit.
2.3 The 74180 IC is a:
Correct Answer: b) 9-bit odd/even parity generator/checker
Explanation: The 74180 is a popular 9-bit parity generator/checker IC that can be configured for either even or odd parity. It has 8 data inputs, one parity input, and both even and odd parity outputs.
2.4 In a parity checker circuit, if the received parity doesn't match the calculated parity, it indicates:
Correct Answer: b) An odd number of bit errors occurred
Explanation: A parity checker compares the received parity bit with the parity calculated from the received data. A mismatch indicates that an odd number of bits (1, 3, 5, etc.) were flipped during transmission.
3.1 Where are parity circuits commonly used?
Correct Answer: c) Both a and b
Explanation: Parity circuits are widely used in both memory systems (to detect errors in RAM) and data communication systems (to detect transmission errors). They provide a simple, low-cost method for error detection.
3.2 The Hamming distance between two code words is:
Correct Answer: a) The number of bits that differ between them
Explanation: Hamming distance is the number of bit positions in which two code words differ. A code with a minimum Hamming distance of 2 can detect single-bit errors (like parity codes), while greater distances allow for error correction.
3.3 Which of the following is a more advanced error detection method than simple parity?
Explanation: Both CRC and Hamming codes are more advanced than simple parity. CRC can detect burst errors and multiple-bit errors, while Hamming codes can not only detect but also correct single-bit errors.
3.4 For a 7-bit data word, how many parity bits are needed in a Hamming code to correct single-bit errors?
Correct Answer: d) 4
Explanation: The number of parity bits (p) needed must satisfy 2^p ≥ p + m + 1, where m is the number of data bits. For m=7, p=4 is needed (2^4=16 ≥ 4+7+1=12). This creates a (11,7) Hamming code.
4.1 What is the even parity bit for the data word 1101101?
Explanation: Count the 1s in 1101101: 1+1+0+1+1+0+1 = 5 (odd). For even parity, the parity bit should make the total count even, so it must be 1 (5+1=6 which is even). Correction: The correct answer should be b) 1.
4.2 A system receives the data 1011010 with odd parity. Is the data correct?
Correct Answer: a) Yes, because the parity is odd
Explanation: Assuming the last bit is the parity bit: data=101101, parity=0. Count of 1s in data is 4 (even). With odd parity, the parity bit should be 1 to make total count odd (4+1=5). Since received parity is 0, the total count is 4 (even), which doesn't match odd parity. Therefore, there's an error. Correction: The correct answer should indicate an error is detected.
4.3 How many possible single-bit errors can a 8-bit data word with parity detect?
Correct Answer: c) 9
Explanation: A single-bit error can occur in any of the 8 data bits or in the parity bit itself. Therefore, there are 9 possible single-bit error positions that parity checking can detect.