Free Octal to Hex Converter – Convert Base-8 to Hexadecimal Online

Convert octal (base-8) numbers to hexadecimal (base-16) instantly. See the complete conversion path through decimal and binary. Uppercase or lowercase output. 100% free.

What Is Octal to Hex Conversion?

Octal to hexadecimal conversion transforms base-8 numbers (digits 0-7) into base-16 numbers (digits 0-9 and A-F). This conversion typically goes through an intermediate decimal or binary step.

Conversion Methods

Method 1: Octal → Decimal → Hex Most straightforward; convert to base-10 first, then to base-16.

Method 2: Octal → Binary → Hex Convert each octal digit to 3 bits, then group bits into sets of 4 for hex.

How to Convert Octal to Hex

Through Decimal (Easiest)

1. Convert octal to decimal using positional values
2. Convert decimal to hex using division by 16

Example: Convert 755₈ to Hex

Step 1: Octal to Decimal

• 755₈ = 7×64 + 5×8 + 5×1
• = 448 + 40 + 5
• = 493₁₀

Step 2: Decimal to Hex

• 493 ÷ 16 = 30 remainder 13 (D)
• 30 ÷ 16 = 1 remainder 14 (E)
• 1 ÷ 16 = 0 remainder 1

Result: 1ED₁₆

Through Binary (Alternative)

Step 1: Octal to Binary

• 7 → 111
• 5 → 101
• 5 → 101
• Result: 111101101₂

Step 2: Binary to Hex (group in 4 bits from right)

• 0001 1110 1101
• = 1 E D
• Result: 1ED₁₆

Common Octal to Hex Conversions

Unix Permissions in Both Bases

Understanding the Number Systems

Octal (Base-8)

• Uses digits: 0, 1, 2, 3, 4, 5, 6, 7
• Each position: 8ⁿ (1, 8, 64, 512...)
• No digits 8 or 9

Hexadecimal (Base-16)

• Uses: 0-9 and A-F (10-15)
• Each position: 16ⁿ (1, 16, 256, 4096...)
• Common in computing

Why Different Bases?

Programming Examples

JavaScript

const octal = '755';
const decimal = parseInt(octal, 8);
const hex = decimal.toString(16).toUpperCase();
// Result: '1ED'

Python

octal = '755'
hex_value = hex(int(octal, 8))
# Result: '0x1ed'

C/C++

int value = 0755;  // Octal literal
printf("%X", value);  // Outputs: 1ED

When to Use Each Base

Octal Is Common For

• Unix file permissions (chmod)
• Some assembly languages
• Legacy documentation

Hex Is Common For

• Memory addresses
• Color codes (#FF5733)
• Byte values
• Debugging

Quick Reference: Small Numbers

Frequently Asked Questions

Why doesn't octal convert directly to hex?

Octal uses 3 bits per digit while hex uses 4 bits. They don't align perfectly, so conversion through decimal or binary rearrangement is needed.

What's the easiest method?

For small numbers, use decimal as intermediate. For large numbers, the binary method avoids big decimal calculations.

Are uppercase and lowercase hex the same?

Yes, A-F and a-f represent the same values. Convention varies by context.

How do I verify my conversion?

Convert back: hex → decimal → octal should give the original number.

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