Question

Convert each of the following octal numbers to binary, hexadecimal, and decimal.

(a) 238
(b) 458
(c) 3718
(d) 25608

a) Define the conversion process for converting octal numbers to binary, hexadecimal, and decimal, ensuring clarity in the steps involved.
b) Instruct the respondent to perform the conversions for each octal number provided in parts (a) to (d).
c) Encourage a brief explanation or justification for each step in the conversion process, demonstrating a thorough understanding of number systems.

Ensure a comprehensive conversion of the specified octal numbers to binary, hexadecimal, and decimal, with detailed explanations for each conversion.

Answer 1

Octal numbers can be converted to binary, hex, and decimal systems using specific methodologies. Each octal digit is transformed into a 3-bit binary string, multiplied by powers of 8 for decimal conversion, and grouped by four for hex conversion after a bin intermediary. Understanding the multiplication and place value principles in different bases ensures accuracy.

Step-by-step explanation:

Conversion of Octal Numbers to Binary, Hexadecimal, and Decimal Systems

The process of converting numbers from the octal system (base-8) to binary (base-2), hexadecimal (base-16), and decimal (base-10) systems involves specific steps for each conversion. Here is a brief outline of how to perform each type of conversion:

1. For octal to binary, convert each octal digit into a 3-bit binary equivalent.
2. For octal to decimal, multiply each digit by 8 raised to the power of its position, starting from right to left, and then sum all the products.
3. For octal to hexadecimal, an intermediary conversion to binary format can ease the process, followed by grouping the binary digits in sets of four and converting to hexadecimal.

Now, let's perform the conversions for each provided octal number:

• Octal 238 to binary would be represented as 010 011 100, to decimal as 158, and to hexadecimal as 9E.
• Octal 458 to binary would be 100 101 1000, to decimal as 303, and to hexadecimal as 12F.
• Octal 3718 to binary would be 011 111 001 1000, to decimal as 1992, and to hexadecimal as 7C8.
• Octal 25608 to binary would be 010 101 110 000 1000, to decimal as 11048, and to hexadecimal as 2B08.

Each step of the conversion process is justified by the respective base system's multiplication and place value principles, ensuring accurate and comprehensive understanding of number systems conversions.