Hexadecimal to Octal Converter

How to Convert Hexadecimal to Octal

Converting hexadecimal numbers to octal is a two-step process involving conversion to decimal as an intermediate step. Here's a comprehensive guide on how to perform this conversion:

Conversion Formula

The process for converting a hexadecimal number to octal involves two main steps:

1. Convert hexadecimal to decimal:
\[ \text{Decimal} = \sum_{i=0}^{n-1} (d_i \times 16^i) \]
2. Convert decimal to octal:
\[ \text{Octal} = \sum_{i=0}^{m-1} (o_i \times 8^i) \]

Where:

• \(d_i\) represents each hexadecimal digit (0-9, A-F)
• \(o_i\) represents each octal digit (0-7)
• \(i\) is the position of the digit (starting from 0 for the rightmost digit)
• \(n\) is the total number of hexadecimal digits
• \(m\) is the total number of octal digits

Conversion Steps

1. Convert the hexadecimal number to decimal.
2. Convert the resulting decimal number to octal.

Example Conversion

Let's convert the hexadecimal number 2A7 to octal.

Step 1: Convert Hexadecimal to Decimal

2A7 in hexadecimal is:

\(2 \times 16^2 + 10 \times 16^1 + 7 \times 16^0 = 512 + 160 + 7 = 679\) in decimal

Step 2: Convert Decimal to Octal

To convert 679 to octal, we divide by 8 repeatedly and read the remainders from bottom to top:

679 ÷ 8 = 84 remainder 7
84 ÷ 8 = 10 remainder 4
10 ÷ 8 = 1 remainder 2
1 ÷ 8 = 0 remainder 1

Reading the remainders from bottom to top gives us 1247.

Final Result

Therefore, 2A7 in hexadecimal = 1247 in octal

Visual Representation

This diagram illustrates the process of converting the hexadecimal number 2A7 to its octal equivalent 1247.