Conversion from Octal to Decimal
Converting a number from octal to decimal involves understanding the positional value of each digit in the octal number. In decimal, each digit's position represents a power of 10, while in octal, each digit's position represents a power of 8. For example, the octal number 247 can be converted to decimal by multiplying the rightmost digit (7) by 8^0 (1), the middle digit (4) by 8^1 (8), and the leftmost digit (2) by 8^2 (64), and then summing up the results (71 + 48 + 2*64 = 7 + 32 + 128 = 167). This process is essential for converting numbers between the octal (base-8) and decimal (base-10) number systems.
Common use cases for converting octal to decimal include programming and computer science applications where octal numbers are used to represent values efficiently in a way that is more compact than decimal numbers. Understanding how to convert between octal and decimal is essential for addressing memory addresses, permissions, and other data representations in computer systems. Additionally, converting between these number systems can also be helpful in mathematical calculations and puzzles that involve numbers in different bases.