Question

Encode the following sentences in ASCII using even parity by adding a parity bit at the high-order end of each character code: a. Does \(100 / 5=20\) ? b. The total cost is \(\$ 725\).

Short answer

Translate each character to ASCII, calculate parity, and add a parity bit to ensure even 1s.

Step-by-step solution

Understand Even Parity

Even parity means that the number of 1s in the binary representation of a character, plus the parity bit, should be even. The parity bit is added at the beginning (high-order end) of the ASCII code.

Convert Characters to ASCII

For each character in the sentences, find its ASCII value and convert it to binary. For example, 'D' corresponds to ASCII 68, which is binary 1000100.

Compute Even Parity Bit

Calculate the number of 1s in each ASCII binary representation and decide on the parity bit. If the number of 1s is odd, the parity bit should be 1 to make it even. If the number of 1s is already even, the parity bit is 0.

Add Parity Bit to ASCII Binary

Insert the parity bit at the beginning of the 7-bit binary ASCII code to form an 8-bit binary number inclusive of the parity. For instance, if the binary of 'D' is 1000100 (which has three 1s, thus odd), add a 1 to the front making it 11000100, ensuring an even number of 1s (4 in this case).

Repeat for Each Character

Perform steps 2-4 for each character in the sentences to encode them fully in even parity. Make sure to add spaces and punctuation among characters to maintain sentence structure.

Key concepts

Even Parity

In communication systems, even parity is a method used to ensure data integrity during transmission. When encoding data, such as characters into binary form, errors can occur. Even parity helps to detect these errors by ensuring the number of '1's in a binary sequence remains even.

Even parity works by adding an additional bit, called the parity bit, to the binary representation of data. If the total count of '1's, including the parity bit, is odd, the parity bit is set to '1'. If it is even, the parity bit is '0'. This simple process ensures that the parity remains even, allowing systems to check for errors by verifying the parity upon receipt.

For example, if a character in binary form has an odd number of '1's, a parity bit of '1' is added, creating an overall even count. This method is lightweight and effective for basic error detection.

Binary Representation

Binary representation is the way computers understand and store data. All data, including characters, numbers, and instructions, are converted into binary, which is a number system using just two digits: 0 and 1. This simplicity aligns with the binary nature of computer systems, which operate using electrical signals that switch between off (0) and on (1).

Each character has a specific ASCII code that is portrayed in binary form. For instance, the character 'A' in ASCII is represented by the decimal number 65, which converts to binary as 1000001. This binary representation is crucial because it forms the basis for various computing operations and encodings, including the addition of parity bits.

Understanding binary representation enables handling of data transformation and manipulation at a fundamental level, making it a critical skill in computer science.

Parity Bit

A parity bit is a binary digit added to data to provide it with basic error-detection capabilities. By appending this single binary digit to a string of data, systems can verify whether a set of bits have been altered during transmission.

The parity bit works by counting the number of '1's in the data. For even parity, if the number of '1's is odd, the parity bit is set to '1', making it even when included in the count. Conversely, if the count is even, the parity bit is set to '0'. This simple addition enhances data integrity, helping to spot if any bit inversions have occurred.

The presence of a parity bit is crucial in places where data accuracy is essential, such as on network communications or data storage systems. A basic understanding can prevent transmission errors from having potentially harmful effects.

Character Encoding

Character encoding is the transformation of text characters into a format that computers can process, such as binary numbers. ASCII, or the American Standard Code for Information Interchange, is the most common character encoding scheme and assigns a unique binary string to each character.

For example, the letter 'A' is encoded as 65 in ASCII, which is represented as 1000001 in binary. ASCII encoding facilitates the exchange and storage of text in computers and networks. By ensuring each character has a standardized binary code, ASCII provides a foundation for further data manipulation, including the addition of parity bits.

Understanding character encoding is vital for the effective transmission of data across different platforms and systems. It allows computers to interpret and properly display text and is particularly useful in debugging and developing software applications where text data is used extensively.