Question

Find the checksum byte for the following ASCII message: "Hello"

Short answer

The checksum byte for the ASCII message 'Hello' is 0x58.

Step-by-step solution

Convert ASCII Characters to Hexadecimal

First, convert each character in the message 'Hello' to its ASCII hexadecimal representation. Use an ASCII table for conversion: 'H' = 48, 'e' = 65, 'l' = 6C, 'l' = 6C, 'o' = 6F.

Calculate the Sum of Hexadecimal Values

Add the hexadecimal values of the characters together: 0x48 + 0x65 + 0x6C + 0x6C + 0x6F = 0x258.

Extract the Lower Byte

Isolate the lower byte of the sum to find the checksum. The sum in hexadecimal is 0x258, so the lower byte is 0x58.

Convert Lower Byte to Checksum

The checksum byte is the lower byte from Step 3, which corresponds to the hexadecimal value 0x58.

Key concepts

ASCII to Hexadecimal Conversion

When working with computer systems, it's necessary to understand the representation of characters. ASCII, which stands for American Standard Code for Information Interchange, assigns a unique decimal number to each character. However, computers work better with hexadecimal numbers, so it's often useful to convert ASCII to hexadecimal. In this conversion, every ASCII character is replaced by its corresponding hexadecimal value that usually consists of one or two hexadecimal digits (ranging from 0 to F). For example, the character 'A' has an ASCII value of 65, which in hexadecimal is 41.

The conversion process involves looking up each character's ASCII decimal value and then converting that number into a hexadecimal number. This step is crucial for several computing tasks, including checksum calculation since it provides a common format for data representation.

Hexadecimal Arithmetic

Hexadecimal arithmetic comes into play when adding, subtracting, or computing checksums with hexadecimal numbers. Since hexadecimal is a base-16 system, each digit can have sixteen possible values (0-9 and A-F), where A represents 10, and F represents 15 in decimal. Adding hexadecimal numbers follows the same principles as in decimal arithmetic, but with a larger base.

When the sum of two hexadecimal digits exceeds 'F' (15 in decimal), you carry over to the next position, much like you would when a sum exceeds 9 in decimal. For example, adding 0x9 and 0x8 yields 0x11 (since 9 + 8 = 17 in decimal). It's important to be comfortable with hexadecimal arithmetic when performing tasks like checksum computations, as these often involve adding hexadecimal values together.

Checksum Byte Computation

A checksum byte is a form of redundancy check, a simple way to detect errors in data. It's essentially a calculated byte that summarizes the data set's overall integrity. In computing checksums, each piece of data is assigned a hexadecimal value, and these values are then added together using hexadecimal arithmetic.

To compute the checksum byte, follow these steps:

• Convert all relevant data into hexadecimal format.
• Add these hexadecimal values together.
• Isolate the lower byte of the sum—it represents the checksum.
• In some cases, this lower byte might be complemented (inverted) to represent the final checksum value.

The 'lower byte' refers to the rightmost two characters in a hexadecimal number after being added together. For example, if the sum is 0x123, the lower byte would be 0x23. The checksum ensures that the data has been transmitted correctly and without error, a critical measure in data integrity and security protocols.