Question

The following two messages are encoded in ASCII using one byte per character and then represented in hexadecimal notation. Are both the messages same? \(436 \mathrm{~F} 6 \mathrm{D} 7075746572436 \mathrm{~F} 6 \mathrm{D} 7075736572\)

Short answer

No, the messages are not the same.

Step-by-step solution

Understanding the Hexadecimal Notation

The given strings represent ASCII values in hexadecimal format. Each pair of hexadecimal digits corresponds to one byte.

Decoding the First Message

The first message in hexadecimal notation is \( 436F6D7075746572 \). Break it down pair by pair: \( 43 \), \( 6F \), \( 6D \), \( 70 \), \( 75 \), \( 74 \), \( 65 \), \( 72 \). These ASCII codes translate to the characters: 'C', 'o', 'm', 'p', 'u', 't', 'e', 'r'.

Decoding the Second Message

The second message in hexadecimal notation is \( 436F6D7075736572 \). Break it down similarly: \( 43 \), \( 6F \), \( 6D \), \( 70 \), \( 75 \), \( 73 \), \( 65 \), \( 72 \). These ASCII codes translate to the characters: 'C', 'o', 'm', 'p', 'u', 's', 'e', 'r'.

Comparing the Two Messages

Now compare the decoded messages: the first message is 'Computer', while the second message is 'Compuser'.

Conclusion

Since the decoded messages are 'Computer' and 'Compuser', they are clearly different.

Key concepts

Understanding Hexadecimal Notation

In the world of computing, hexadecimal notation is a base-16 number system. It uses sixteen distinct symbols: the numbers 0 to 9 and the letters A to F. Each of these symbols corresponds to a value between 0 and 15. This system is particularly beneficial for encoding large amounts of data compactly. It's often used in programming and digital electronics because it aligns neatly with byte boundaries in the binary system. Each hexadecimal digit represents four binary digits (bits), and two hexadecimal digits together represent one byte. In ASCII encoding, each hex pair corresponds to a character.

For instance, in an ASCII encoded message, the hexadecimal pair '43' converts to the decimal number 67, which represents the character 'C'. Hexadecimal notation is a concise way to display binary-coded values, making it easier to read and understand, especially in tasks involving data encoding or decoding. Understanding this notation is crucial in deciphering encoded text, like the strings in our original exercise.

Character Encoding and ASCII

Character encoding translates characters into a format that computers can store and manipulate. ASCII (American Standard Code for Information Interchange) is one of the most widely used encoding systems. In ASCII, each character is assigned a unique numeric value. This encoding scheme uses seven bits per character, allowing for 128 possible characters, including letters, digits, punctuation marks, and control codes.

When text is encoded using ASCII, each character is represented by a number. In hexadecimal notation, these numbers are expressed using base-16 digits. For example, the character 'A' is represented by the decimal number 65, which is '41' in hexadecimal. Similarly, 'C' in ASCII is the number 67, or '43' in hex.

This system is pivotal for ensuring consistent character representation across different devices and platforms. In our exercise, understanding ASCII allows us to decode the hexadecimal strings back to readable text. This is why recognizing the relationship between hexadecimal notation and ASCII is essential for processing text data effectively.

Breaking Down Problem Solving with Encoding

Problem solving in character encoding involves systematically decoding or encoding text into the desired format. This requires careful attention to the encoding schemes and notation used. The original exercise showcased a problem-solving scenario: determining if two encoded messages are the same despite their hexadecimal differences.

To tackle such a problem, one should:

• Understand the encoding system: Know what ASCII is and how hexadecimal notation fits in.
• Identify each hexadecimal pair and its corresponding ASCII character.
• Translate the entire string of hexadecimal notations to reveal the character sequence.
• Compare the decoded sequences to see if they match.

Each of these steps requires keen observation and a conversion of abstract numbers (hexadecimal) back into a recognizable language (ASCII). Through solving such problems, you not only practice conversion skills but also reinforce your understanding of how data representation and character encoding works. This detailed approach was reflected in our exercise when we methodically converted the sequences and found two different messages, demonstrating the analytical process in problem solving.