Question

Are problems or shortanswer questions. Given the following 8-bit code, what is the parity bit if odd parity is being used? a. 11100010 b. 10101010 c. 11111111 d. 00000000 e. 11101111

Short answer

a: 1, b: 1, c: 1, d: 1, e: 0

Step-by-step solution

Count the Number of 1's

For each given 8-bit code, count the number of bits that are 1s. This count determines whether the current number of bits is even or odd.

Determine Required Parity Bit

Odd parity means the total number of 1's (including the parity bit) should be odd. If the count from Step 1 is even, the parity bit should be 1 to make it odd. Conversely, if the count is odd, the parity bit should be 0 to maintain the odd number of 1s.

Analyze Each Option

- a. 11100010: There are 4 ones. It's even, so the parity bit should be 1. - b. 10101010: There are 4 ones. It's even, so the parity bit should be 1. - c. 11111111: There are 8 ones. It's even, so the parity bit should be 1. - d. 00000000: There are 0 ones. It's even, so the parity bit should be 1. - e. 11101111: There are 7 ones. It's odd, so the parity bit should be 0.

Key concepts

Odd Parity

Odd parity is a technique used in data transmission to ensure that the total number of 1s in a set of binary data is always odd. This is achieved by adding an extra bit, known as the parity bit, to the end of a string of binary data. The primary purpose of using odd parity is to detect errors in data. When data is transmitted, unwanted changes such as bit flips can occur due to noise or other interference. The odd parity system allows us to verify that the data has not been altered by ensuring an odd number of 1s end up in the transmission. If the number of 1s is even when odd parity is expected, it means there was a transmission error. This system adds a layer of error-checking without too much complexity.

8-bit Code

An 8-bit code refers to a sequence of 8 bits where each bit is a binary digit, either 0 or 1. The 8-bit architecture is prevalent in computing and data transmission because it is straightforward and efficient. In an 8-bit system, there are 256 possible combinations of bits, ranging from 00000000 to 11111111. This flexibility allows the representation of various values, whether numbers, characters, or other data types. Each bit in the 8-bit code holds a power of 2, giving the lowest bit value as 1 and the highest as 128 (2 extsuperscript{7}). This concept is fundamental in computing and is the basis for understanding more complex data structures. With parity bits involved, the 8-bit code becomes crucial because the parity bit aims to control the count of 1s in these configurations.

Counting Ones

Counting the number of 1s in an 8-bit code is a critical step in determining the correct parity bit. This step is the foundation for applying parity, ensuring data integrity during transmission. Here's how it works:

• Review the given 8-bit sequence.
• Count how many bits are '1' in this sequence.

The count of these 1s dictates whether the sequence currently maintains odd parity or needs an adjustment. As this exercise shows, if the number of 1s in a sequence is even, a parity bit of '1' will make it odd. If the count is already odd, a parity bit of '0' will suffice to maintain the desired oddness.

Parity Calculation

Calculating the parity involves a simple decision-making process once you have counted the number of 1s. This process includes determining whether or not the data string using an 8-bit code needs a parity bit of 1 or 0 to achieve odd parity. Here's a structured approach:

• If the total number of 1s (excluding the parity bit) is even, you add a parity bit of 1.
• If the total number of 1s is odd, you add a parity bit of 0.

This logic ensures that with the parity bit included, the entire string of bits has an odd number of 1s. Parity calculation is essential as a simplistic error-checking mechanism that ensures the bit data integrity in communications and storage scenarios.