Octal to Hexadecimal Converter

How to Convert Octal to Hexadecimal

Converting octal numbers to hexadecimal is a two-step process that involves first converting the octal number to decimal, and then converting the decimal to hexadecimal. Here's a comprehensive guide on how to perform this conversion:

Conversion Formula

The process involves two main formulas:

1. Octal to Decimal: \[ Decimal = \sum_{i=0}^n d_i \times 8^i \]
2. Decimal to Hexadecimal: Repeatedly divide by 16 and collect remainders

Where:

• \(d_i\) represents each octal digit (0-7)
• \(i\) is the position of the digit from right to left, starting at 0
• \(n\) is the number of digits minus 1

Conversion Steps

1. Convert the octal number to decimal using the first formula.
2. Convert the resulting decimal to hexadecimal by repeatedly dividing by 16 and collecting remainders.
3. Read the remainders from bottom to top to get the hexadecimal number.

Example Conversion

Let's convert the octal number 253 to hexadecimal.

Step 1: Convert Octal to Decimal

\(2 \times 8^2 + 5 \times 8^1 + 3 \times 8^0 = 128 + 40 + 3 = 171_{10}\)

Step 2: Convert Decimal to Hexadecimal

171 ÷ 16 = 10 remainder 11 (B)
10 ÷ 16 = 0 remainder 10 (A)

Final Result

Reading the remainders from bottom to top, we get:

Therefore, 253 in octal = AB in hexadecimal

Visual Representation

This diagram illustrates the process of converting the octal number 253 to its hexadecimal equivalent AB, with the intermediate decimal representation of 171.