HEX HeroConvert 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.
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.
Convert Each Hex Digit to 4-Bit Binary
Replace each hexadecimal digit with its 4-bit binary nibble.
0x1ED → 0001 1110 1101
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
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
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.
VAXVAX/VMS Systems
VAX computers (1977-2000) inherited PDP-11's octal tradition. System dumps and debuggers displayed values in octal.
UNIXClassic Unix v6 & v7
Early Unix (1970s) source code used octal constants throughout. The Lions' Commentary on Unix v6 is entirely in octal.
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
Common Hex Values
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.