Convert Hex to Octal

Enter your hexadecimal values below—one per line—and get instant octal conversions. Whether you're working with legacy systems, analyzing tar archive headers, or exploring vintage computing formats, this tool handles hex-to-octal conversion with ease.

HEXADECIMAL

Enter hexadecimal values to convert

OCTAL

Outputs octal (base-8) representation

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How to convert Hexadecimal to Octal - a step by step tutorial

Convert modern hex values to legacy octal notation. Master nibble-to-binary expansion and regrouping into 3-bit octal digits for retro computing projects.

Using This Tool

Hex-to-octal conversion uses binary as a bridge. Convert hex → binary → octal using different bit groupings.

1

Convert Each Hex Digit to 4-Bit Binary

Replace each hexadecimal digit with its 4-bit binary nibble.

0x1ED → 0001 1110 1101

2

Regroup into 3-Bit Groups

Starting from right, group binary into sets of 3 bits. Pad left side with zeros if needed.

000 111 101 101

3

Convert Each 3-Bit Group to Octal

Replace each 3-bit group with its octal digit (0-7).

000=0, 111=7, 101=5, 101=5

4

Combine and Format

Write octal digits together. Drop leading zeros for standard form.

0x1ED₁₆ = 755₈

Hex to Octal for Retro Computing

Classic computers from the 1960s-1980s used octal extensively. Converting modern hex values to octal helps understand historical documentation and vintage systems.

PDP-11DEC PDP-11 Memory Addressing

The iconic PDP-11 (1970-1990s) used octal for all memory addresses and machine code. Converting modern hex addresses aids in reading vintage assembly listings.

Modern: 0x1000 (hex) → 010000 (octal)
PDP-11 notation: 010000₈ = 4096₁₀ bytes
// Common PDP-11 addresses
0177560₈ (keyboard status) = 0xFFF0₁₆
0177776₈ (program counter) = 0xFFFE₁₆

VAXVAX/VMS Systems

VAX computers (1977-2000) inherited PDP-11's octal tradition. System dumps and debuggers displayed values in octal.

VAX memory page: 0x200₁₆ = 1000₈ (512 bytes)
Protection code: 0xF₁₆ = 17₈ (URWE bits)
// VMS privilege masks
SYSPRV: 0x1₁₆ = 01₈
TMPMBX: 0x40₁₆ = 100₈

UNIXClassic Unix v6 & v7

Early Unix (1970s) source code used octal constants throughout. The Lions' Commentary on Unix v6 is entirely in octal.

/* K&R C escape sequences */
\\033 (ESC) = 0x1B hex = 27 decimal
\\177 (DEL) = 0x7F hex = 127 decimal
// inode structure offsets
i_mode at 0₈, i_nlink at 2₈, i_uid at 4₈

Why Convert Hex to Octal Today

📚

Reading Classic Computing Books

The C Programming Language (K&R), Lions' Commentary on Unix, and PDP-11 manuals use octal. Converting modern hex values (from emulators, debuggers) to octal helps cross-reference with original documentation.

🕹️

Retro Gaming & Emulation

Classic arcade games and early home computers (Atari, Commodore) sometimes used octal in schematics. Hex dumps from emulators convert to octal for matching service manuals and repair documentation.

🔧

Vintage System Restoration

Hobbyists restoring PDP-11, VAX, or Data General Nova systems need octal for diagnostics. Modern USB analyzers and logic probes display hex; octal conversion matches original equipment front-panel displays.

🎓

Computer Science Education

Some CS curricula teach number systems using historical context. Students learning about early Unix or minicomputers convert between hex (modern standard) and octal (historical standard) to understand computing evolution.

💾

Data Recovery from Old Media

9-track tapes, DECtape, and paper tape used octal addressing. Modern disk imaging tools output hex; converting to octal helps identify tape block boundaries and error markers from original format specifications.

🏛️

Computer History Preservation

Museums and archives digitizing old computer documentation scan octal listings. Hex-to-octal conversion verifies scanned values against checksums and validates transcription of historical source code for preservation projects.

Hex to Octal Conversion Reference

Quick lookup for vintage computing and legacy system work.

Single Hex Digit

0x00(000)
0x11(001)
0x77(111)
0x810(001 000)
0xF17(001 111)
0x1020(010 000)

Common Hex Values

0x4010064 decimal
0x7F177DEL character
0xFF377255 decimal
0x1B33ESC character
0x2001000512 decimal
0xFFF777712-bit max

Why Did Old Computers Use Octal?

👁️ Octal Matched Word Sizes

Early minicomputers (PDP-8, PDP-11) used 12-bit, 18-bit, and 36-bit words—all divisible by 3 but not 4. Octal (3 bits per digit) perfectly represented these word sizes. Hex (4 bits) would have awkward partial nibbles.

🖥️ Front Panel Switches

Computer front panels had toggle switches in groups of 3 (for octal entry). Operators could quickly set addresses in octal by flipping switch triplets. PDP-11 panels grouped lights and switches in sets of 3, making octal natural.

📖 Easier Mental Math

In the 1960s-70s, octal multiplication/division was taught alongside hex. Many engineers found octal-to-binary conversion simpler (3 bits vs 4). DEC manuals, Bell Labs Unix docs, and IBM 7090 materials all standardized on octal.

🔄 The Shift to Hex

Hexadecimal became dominant with 8-bit microprocessors (1970s Intel 8080, Zilog Z80) and 16/32-bit systems. Byte-oriented architectures (8, 16, 32, 64 bits—all divisible by 4) favored hex. By the 1980s, hex replaced octal everywhere except Unix file permissions.

Hex to Octal: Retro Computing FAQs

Why do PDP-11 manuals show addresses in octal like 177560?

The PDP-11 used 16-bit addressing (0-177777 octal = 0x0000-0xFFFF hex). DEC chose octal because it aligns with 3-bit groupings, matching the machine's instruction format and front-panel switch layout. 177560 octal = 0xFFF0 hex = 65520 decimal.

How to read Unix v6 source code that uses octal constants?

Early Unix (1975) used octal everywhere. When you see 0177777, it's octal (leading 0). Convert to hex for modern understanding: 0177777₈ = 0xFFFF₁₆. Lions' Commentary is a masterclass in reading octal-heavy C code.

Can I use a modern hex debugger to debug vintage octal systems?

Yes! Convert breakpoints and memory addresses: hex 0x2000 = octal 020000 when entering addresses into simulators like simh (which accepts octal). Most PDP-11 emulators let you toggle between hex and octal display modes for convenience.

What's the deal with \\033 vs \\x1B for escape sequences?

Both represent ESC (27 decimal). \\033 is octal (K&R C style, pre-1980s), \\x1B is hex (ANSI C89 onward). Old Unix terminal code uses \\033; modern code prefers \\x1B. Same character, different notation epochs.

Why did IBM mainframes use hex while DEC used octal?

IBM System/360 (1964) was byte-oriented (8-bit bytes), making hex natural. DEC minicomputers (PDP series) had 12/18/36-bit words, favoring octal. This split lasted decades—DEC/Unix world used octal, IBM/PC world used hex. Intel x86 (1978) followed IBM's hex convention.

Is there any advantage to octal over hex today?

Only for Unix file permissions (chmod) where 3-bit groups (rwx) map cleanly to octal. Otherwise, hex dominates. However, octal literacy remains valuable for: understanding computer history, reading classic texts, and maintaining legacy systems still running in industrial/military applications.

Convert hexadecimal numbers to decimal numbers.

Convert hexadecimal numbers to binary numbers.

HEX to octal conversion table.

OCTAL to hex conversion table.


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