Question

Match the name of the technique with the algorithm. A. Even parity B. Odd parity C. Check digits D. Error-correcting codes E. Parity bit The number of 1 bits plus the parity bit is odd.

Short answer

B. Odd parity.

Step-by-step solution

Understand Each Term

Begin by understanding the descriptions of all the given techniques. - **Even parity** means the number of 1s in the data, including the parity bit, is even. - **Odd parity** means the number of 1s in the data, including the parity bit, is odd. - **Check digits** are numbers added to a series of numbers to ensure the entire sequence is correct. - **Error-correcting codes** are used to detect and correct errors in data transmission. - **Parity bit** is a bit added to data to make the number of set bits either even or odd.

Analyze the Given Definition

The definition provided is: "The number of 1 bits plus the parity bit is odd." This definition matches the description of **Odd parity**, where a parity bit is used to ensure the total count of 1s (including the parity bit) is odd.

Match the Technique to the Definition

Based on the analysis in Step 2, the definition corresponds directly to **B. Odd parity**. In odd parity, the parity bit is set in such a way that the total number of 1 bits is odd.

Key concepts

Even Parity

Even parity is a data integrity technique that helps ensure the correct transmission and storage of data. It involves adding an extra bit, known as the parity bit, to a set of binary data. The goal is to make the total number of 1s in the data—including the parity bit—an even number. This way, if there is a transmission error that causes a single bit to flip (either 0 to 1 or 1 to 0), the receiver can detect the error because the total number of 1s will no longer match the expected even count.

For example, if you have binary data like 1010, which contains two 1s, the parity bit added for even parity would be 0 to keep it even. However, if the data were 1011 (which is three 1s), a parity bit of 1 would be added to make the total count four, which is even.

Even parity is simple and effective for catching single-bit errors in data transmission. However, it cannot correct errors; it can only alert the system that an error has occurred.

Check Digits

Check digits are very common in everyday life, making sure data entry mistakes can be spotted. They are most often used in numbers like credit card numbers or product barcodes. Here's how they work: a check digit is added to a string of numbers based on a specific algorithm. It helps in verifying the integrity of the data. If the data is mistyped, the check digit will fail to match what is expected, signaling an error.

This technique uses algorithms specific to the kind of numbers. For example, credit cards use the Luhn algorithm to determine if a string of numbers is valid based on the final check digit. If even a single number is entered incorrectly, the check digit won't match, alerting the system to a possible mistake.

Remember, check digits are great for detecting many types of errors but not for correcting them. They are a preventive measure to catch data entry errors early, minimizing problems.

Error-Correcting Codes

Error-correcting codes go a step beyond simply detecting errors. They are designed to both detect and correct errors within data, making them extremely valuable for reliable communication systems. These codes transform the original data into a longer bitstream that enables detection of up to a certain number of errors and can also repair these errors.

Commonly used error-correcting codes include Reed-Solomon and Hamming codes, each suited for different applications. Reed-Solomon codes, for instance, are widely used in CDs, DVDs, and Blu-ray discs. They help correct scratches and other physical damage. Hamming codes are often used in computer memory systems.

Error-correcting codes are crucial in situations where data integrity is critical, such as in data storage devices and digital communications. They ensure the data received is the same as the data sent, even in the presence of noise or other impairments.

Parity Bit

A parity bit is essentially a small insurance policy for data accuracy in digital communication. It is an additional bit attached to a string of binary data to help detect errors in the data. By ensuring that the total number of bits with a value of 1 is even or odd, as predetermined, the parity bit helps identify transmission errors.

The parity bit is fundamental in both even and odd parity schemes:

• In even parity, the parity bit makes the total count of 1s even.
• In odd parity, the parity bit makes the total count of 1s odd.

When the receiving system counts bits and discovers the parity is incorrect, it knows an error has occurred. However, it’s important to note that while parity bits can detect that an error occurred, they can't specify where the error is nor can they correct it.

Parity bits are the simplest form of error detection and are widely used in memory storage and communications to catch transmission errors in real-time.