What is two's complement?

It's how modern CPUs represent signed (positive and negative) integers in binary. To get the negative of a number, you flip every bit and add 1 — that's the encoding. This calculator stays in non-negative-value territory because two's complement only makes sense at a specific bit width (8-bit, 16-bit, 32-bit, etc.). Signed arithmetic at the bit level is a separate rabbit hole worth its own deep dive.

Why is binary used at the hardware level?

Because computer hardware uses two voltage levels (on/off, high/low) to represent 0 and 1 — way simpler and more reliable than decimal would be (you'd need 10 distinguishable voltage levels, which is asking for trouble at high speeds). Everything digital — text, images, programs, this very webpage — ultimately reduces to long sequences of binary at the silicon level.

What is the largest base supported here?

Bases 2 through 16 — binary, octal, decimal, hexadecimal. Specialized encodings like Base32 (Google Authenticator codes) and Base64 (embedding binary in text emails or URLs) are technically encodings rather than pure positional numeral systems, so they're not handled here. Use a dedicated Base64 encoder for those.

What do the letters A-F mean in hex?

Hexadecimal uses 16 digits total. The first ten are familiar 0-9, the remaining six are A (10), B (11), C (12), D (13), E (14), and F (15). Hex is case-insensitive — 'FF' and 'ff' mean the same value. The convention: lowercase for URLs and lowercase-friendly contexts, uppercase for constants and the kind of code where it'll be read out loud.

Why are RGB colors written as 6 hex characters?

Each color channel (Red, Green, Blue) lives in one byte (values 0-255), which is exactly two hex digits. So a 24-bit color is 3 bytes = 6 hex characters in the form #RRGGBB. The short form #RGB is CSS shorthand that doubles each digit — #F00 expands to #FF0000 (pure red), but only when the full version would have matching pairs in each channel.

What about octal — is it still used?

Occasionally, yes. Octal (base 8) was big on older computers because it maps cleanly to 3-bit groups, which was convenient on 6-bit or 12-bit architectures. Today it mostly survives in Unix file permissions (chmod 755 means owner rwx, group rx, others rx). Outside that one corner of the world, octal is mostly legacy these days — hex won.

How does this calculator help web developers?

Hex is the standard CSS color format. When a design tool hands you a color in RGB, the base converter gives you the hex equivalent in one click for pasting into stylesheets. It also helps with alpha values that sometimes appear as 8-character hex (like #FF000080, where the last two digits are 50 percent alpha). Saves five seconds every time, but those seconds add up.

Premium Converters

Base Converter

Utility

Convert integers between binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16) — built for programmers debugging memory addresses, bitmasks, and hex colors.

Utility

Base Converter

Generated on May 23, 2026

Value

From Base

Quick Answer

Convert integers between binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16) — built for programmers debugging memory addresses, bitmasks, and hex colors.

Overview — Base Converter

Utility

A base converter translates integer numbers between positional numeral systems — binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16). Each system expresses the same underlying value using different digits and place values. This tool is essential for programmers working with memory addresses and bitmasks, electronics engineers reading logic levels, computer-science students learning number theory, and web designers decoding hex colors.

Formula

Value = Σ(digit × base^position), with positions counted from 0 on the right. To convert, first parse to decimal, then repeatedly divide by the target base and collect remainders.

255 (FF hex) = one byte's maximum value — the cap for each RGB channel in a web color.

65,535 (FFFF hex) = max 16-bit unsigned integer — the original Internet port number range.

16,777,215 (FFFFFF hex) = max 24-bit color = pure white #FFFFFF.

By Muhammad Salman SaleemUpdated: May 23, 2026MethodologyFree, no sign-upRuns in your browser — your data stays private

From the editors — what to know before you start

It's 2am, you're a Karachi backend developer staring at a stack trace that includes a memory address like 0x7FFFFA88E2C0, and you're trying to figure out roughly where in memory that lives. Or you're debugging a bitmask permission flag — the API returns 0b10110101 and you need to know what that means in decimal so you can grep the docs. Or you're a CS undergrad doing the binary-to-hex conversion homework that every CS101 course assigns by tradition. This converter does instant translation between binary, octal, decimal, and hexadecimal — type into any one field, the other three update live. Hex is the workhorse for any low-level work because one hex digit equals exactly 4 bits (half a byte), so a byte fits in two hex digits and a 32-bit integer fits in eight. That alignment is why memory addresses, RGB color codes, and bitwise flags are universally written in hex — binary is too verbose, decimal doesn't align to byte boundaries. Octal mostly survives in one place: Unix file permissions (chmod 755 means owner rwx, group rx, others rx — that 7 is 111 in binary, 5 is 101). Knowing this stops you from memorizing chmod combinations as magic numbers. Worth knowing: 255 (one byte's max), 65,535 (two bytes), and 16,777,215 (three bytes = max RGB color) come up often enough that recognizing them in any base saves debugging time.

Pro tips most people learn the hard way

One hex digit equals exactly 4 bits. A byte is two hex digits. A 32-bit integer is eight hex digits. This alignment is why every memory address, RGB color, and bitmask flag in the world is written in hex — binary takes too much screen space, decimal doesn't snap to byte boundaries. Hex is the right tool for byte-level work.
chmod 755 stops being a magic number once you see octal. 7 is 111 in binary (rwx all on), 5 is 101 (read and execute, no write). Each octal digit maps to one permission set: owner, group, others. Once this clicks, you can construct any chmod value from the desired permissions instead of memorizing the common ones.
0x7FFF in hex is 32,767 in decimal — the maximum value of a signed 16-bit integer. 0xFFFF is 65,535, max unsigned 16-bit. 0x7FFFFFFF is 2.1 billion, max signed 32-bit. 0xFFFFFFFF is 4.3 billion, max unsigned 32-bit. Recognizing these boundary values speeds up debugging integer-overflow bugs by a lot.
Pro tip: when reading bitwise flags from an API or log, convert to binary first. A status byte of 0xA7 is 10100111 in binary, which means flags 0, 1, 2, 5, and 7 are set. That's instantly more readable than 167 (decimal), which tells you nothing about which individual bits are on or off.
Octal is mostly dead outside chmod. It survived because Unix permissions map cleanly to 3-bit groups, but for modern bitwise work, hex won. If you see octal in a new project, it's probably copy-pasted from old documentation and worth converting to hex for the next developer's sanity.

?What is the Base Converter?

The Formula

Value = Σ(digit × base^position), with positions counted from 0 on the right. To convert, first parse to decimal, then repeatedly divide by the target base and collect remainders.

In any positional system, each digit is multiplied by its base raised to the power of its position, and the products are summed. The rightmost digit is position 0, the next is position 1, and so on. To move between bases, the calculator parses the input into a single decimal value, then repeatedly divides by the target base — the remainders at each step become the target-base digits, read from bottom to top.

Number Base Reference — Decimal, Binary, Octal & Hexadecimal

Common integer values in the 4 most-used number bases — essential for programming and computer science.

Decimal	Binary	Octal	Hexadecimal
0	0	0	0
1	1	1	1
7	111	7	7
8	1000	10	8
10	1010	12	A
15	1111	17	F
16	10000	20	10
32	100000	40	20
64	1000000	100	40
100	1100100	144	64
128	10000000	200	80
255	11111111	377	FF
256	100000000	400	100
1024	10000000000	2000	400
65535	—	177777	FFFF
16777215	—	—	FFFFFF

Put It in Perspective

255 (FF hex) = one byte's maximum value — the cap for each RGB channel in a web color.

65,535 (FFFF hex) = max 16-bit unsigned integer — the original Internet port number range.

16,777,215 (FFFFFF hex) = max 24-bit color = pure white #FFFFFF.

Unix file permissions (chmod 755) use octal: 7 = rwx (read+write+execute), 5 = r-x.

Practical Examples

255 in decimal equals FF in hex, 11111111 in binary, and 377 in octal — the maximum value of a single byte.

1024 in decimal equals 400 in hex and 10000000000 in binary — 2^10, the classic computing boundary.

Hex color #FF0000 equals RGB (255, 0, 0), which is pure red — each hex pair represents one 0-255 color channel.

Binary 1010 equals decimal 10 — a small illustrative example useful for teaching.

Memory address 0x7FFFFF in hex equals 8,388,607 in decimal — useful when debugging low-level code or embedded systems.

Unicode code point U+1F600 (the grinning face emoji) is hex 1F600 = decimal 128,512 — used when working with character encoding.

Frequently Asked Questions

Because one hex digit equals exactly 4 bits (half a byte), so a full byte fits in two hex digits and a 32-bit integer fits cleanly in 8. That alignment makes hex the cleanest way to read memory dumps, RGB color values, and raw bit patterns. Binary is way too verbose (8 characters per byte) and decimal doesn't align with byte boundaries at all — hex is the Goldilocks zone for low-level work.

Popular Conversions

Jump to a ready-made conversion — useful for quick reference and sharing:

Browse all Utility

Unix Timestamp Converter

Translate Unix epoch timestamps (seconds or milliseconds since Jan 1 1970 UTC) to readable ISO, UTC, and local-timezone dates — auto-detects format and handles the Y2038 problem.

Color Converter

Translate colors between HEX, RGB, and HSL with a live swatch preview — built for CSS work, brand palette design, and converting Tailwind shades between formats.

Word Counter

Live word, character, sentence, and paragraph counter with reading and speaking time estimates — ideal for essays, blog SEO, tweets within 280 chars, and timed speeches.

Case Converter

Instantly convert text between UPPERCASE, lowercase, Title Case, Sentence case, camelCase, PascalCase, snake_case, and kebab-case — ideal for variable renaming, URL slugs, and headings.

Password Generator

Generate cryptographically secure random passwords (6 to 64 chars) using the browser's Web Crypto API, with strength meter and optional uppercase, digits, and symbol character sets.

Text Reverser / Palindrome Checker

Reverse any text character-by-character or word-by-word, plus check classic palindromes like "A man, a plan, a canal: Panama" while ignoring spaces, punctuation, and case.

QR Code Generator

Create QR codes from URLs, text, Wi-Fi, contact cards, email, phone, SMS, and locations. Free PNG and SVG download.

Barcode Generator

Generate Code 128, EAN-13, UPC-A, Code 39, ITF-14, and more. Free PNG and SVG download with format-aware validation.

Browse all Utility calculators & converters

See every tool in this category, plus FAQs and category-specific guides.

Browse other categories

Islamic9 Financial14 Gold & Silver8 Health25 Unit19 Date & Time9 Math21 Construction22 Fun12

Premium Converters

Base Converter

Utility

Convert integers between binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16) — built for programmers debugging memory addresses, bitmasks, and hex colors.

Utility

Base Converter

Generated on May 23, 2026

Value

From Base

Quick Answer

Convert integers between binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16) — built for programmers debugging memory addresses, bitmasks, and hex colors.

Overview — Base Converter

Utility

Formula

Value = Σ(digit × base^position), with positions counted from 0 on the right. To convert, first parse to decimal, then repeatedly divide by the target base and collect remainders.

255 (FF hex) = one byte's maximum value — the cap for each RGB channel in a web color.

65,535 (FFFF hex) = max 16-bit unsigned integer — the original Internet port number range.

16,777,215 (FFFFFF hex) = max 24-bit color = pure white #FFFFFF.

By Muhammad Salman SaleemUpdated: May 23, 2026MethodologyFree, no sign-upRuns in your browser — your data stays private

From the editors — what to know before you start

Pro tips most people learn the hard way

One hex digit equals exactly 4 bits. A byte is two hex digits. A 32-bit integer is eight hex digits. This alignment is why every memory address, RGB color, and bitmask flag in the world is written in hex — binary takes too much screen space, decimal doesn't snap to byte boundaries. Hex is the right tool for byte-level work.
chmod 755 stops being a magic number once you see octal. 7 is 111 in binary (rwx all on), 5 is 101 (read and execute, no write). Each octal digit maps to one permission set: owner, group, others. Once this clicks, you can construct any chmod value from the desired permissions instead of memorizing the common ones.
0x7FFF in hex is 32,767 in decimal — the maximum value of a signed 16-bit integer. 0xFFFF is 65,535, max unsigned 16-bit. 0x7FFFFFFF is 2.1 billion, max signed 32-bit. 0xFFFFFFFF is 4.3 billion, max unsigned 32-bit. Recognizing these boundary values speeds up debugging integer-overflow bugs by a lot.
Pro tip: when reading bitwise flags from an API or log, convert to binary first. A status byte of 0xA7 is 10100111 in binary, which means flags 0, 1, 2, 5, and 7 are set. That's instantly more readable than 167 (decimal), which tells you nothing about which individual bits are on or off.
Octal is mostly dead outside chmod. It survived because Unix permissions map cleanly to 3-bit groups, but for modern bitwise work, hex won. If you see octal in a new project, it's probably copy-pasted from old documentation and worth converting to hex for the next developer's sanity.

?What is the Base Converter?

The Formula

Value = Σ(digit × base^position), with positions counted from 0 on the right. To convert, first parse to decimal, then repeatedly divide by the target base and collect remainders.

Number Base Reference — Decimal, Binary, Octal & Hexadecimal

Common integer values in the 4 most-used number bases — essential for programming and computer science.

Decimal	Binary	Octal	Hexadecimal
0	0	0	0
1	1	1	1
7	111	7	7
8	1000	10	8
10	1010	12	A
15	1111	17	F
16	10000	20	10
32	100000	40	20
64	1000000	100	40
100	1100100	144	64
128	10000000	200	80
255	11111111	377	FF
256	100000000	400	100
1024	10000000000	2000	400
65535	—	177777	FFFF
16777215	—	—	FFFFFF

Put It in Perspective

255 (FF hex) = one byte's maximum value — the cap for each RGB channel in a web color.

65,535 (FFFF hex) = max 16-bit unsigned integer — the original Internet port number range.

16,777,215 (FFFFFF hex) = max 24-bit color = pure white #FFFFFF.

Unix file permissions (chmod 755) use octal: 7 = rwx (read+write+execute), 5 = r-x.

Practical Examples

255 in decimal equals FF in hex, 11111111 in binary, and 377 in octal — the maximum value of a single byte.

1024 in decimal equals 400 in hex and 10000000000 in binary — 2^10, the classic computing boundary.

Hex color #FF0000 equals RGB (255, 0, 0), which is pure red — each hex pair represents one 0-255 color channel.

Binary 1010 equals decimal 10 — a small illustrative example useful for teaching.

Memory address 0x7FFFFF in hex equals 8,388,607 in decimal — useful when debugging low-level code or embedded systems.

Unicode code point U+1F600 (the grinning face emoji) is hex 1F600 = decimal 128,512 — used when working with character encoding.

Frequently Asked Questions

Popular Conversions

Jump to a ready-made conversion — useful for quick reference and sharing:

Browse all Utility

Unix Timestamp Converter

Translate Unix epoch timestamps (seconds or milliseconds since Jan 1 1970 UTC) to readable ISO, UTC, and local-timezone dates — auto-detects format and handles the Y2038 problem.

Color Converter

Translate colors between HEX, RGB, and HSL with a live swatch preview — built for CSS work, brand palette design, and converting Tailwind shades between formats.

Word Counter

Live word, character, sentence, and paragraph counter with reading and speaking time estimates — ideal for essays, blog SEO, tweets within 280 chars, and timed speeches.

Case Converter

Instantly convert text between UPPERCASE, lowercase, Title Case, Sentence case, camelCase, PascalCase, snake_case, and kebab-case — ideal for variable renaming, URL slugs, and headings.

Password Generator

Generate cryptographically secure random passwords (6 to 64 chars) using the browser's Web Crypto API, with strength meter and optional uppercase, digits, and symbol character sets.

Text Reverser / Palindrome Checker

Reverse any text character-by-character or word-by-word, plus check classic palindromes like "A man, a plan, a canal: Panama" while ignoring spaces, punctuation, and case.

QR Code Generator

Create QR codes from URLs, text, Wi-Fi, contact cards, email, phone, SMS, and locations. Free PNG and SVG download.

Barcode Generator

Generate Code 128, EAN-13, UPC-A, Code 39, ITF-14, and more. Free PNG and SVG download with format-aware validation.

Browse all Utility calculators & converters

See every tool in this category, plus FAQs and category-specific guides.

Browse other categories

Islamic9 Financial14 Gold & Silver8 Health25 Unit19 Date & Time9 Math21 Construction22 Fun12

Base Converter — integers between binary (base 2) | Premium Converters

Premium Converters

Premium Converters

Base Converter

Base Converter

Overview — Base Converter

From the editors — what to know before you start

Pro tips most people learn the hard way

?What is the Base Converter?

The Formula

Number Base Reference — Decimal, Binary, Octal & Hexadecimal

Put It in Perspective

Practical Examples

Frequently Asked Questions

Popular Conversions

Embed this calculator on your site

Browse other categories

Premium Converters

Base Converter

Base Converter

Overview — Base Converter

From the editors — what to know before you start

Pro tips most people learn the hard way

?What is the Base Converter?

The Formula

Number Base Reference — Decimal, Binary, Octal & Hexadecimal

Put It in Perspective

Practical Examples

Frequently Asked Questions

Popular Conversions

Embed this calculator on your site

Browse other categories

Premium Converters

Premium Converters

Base Converter

Base Converter

Overview — Base Converter

From the editors — what to know before you start

Pro tips most people learn the hard way

?What is the Base Converter?

The Formula

Number Base Reference — Decimal, Binary, Octal & Hexadecimal

Put It in Perspective

Practical Examples

Frequently Asked Questions

Why is hexadecimal so popular in programming?

What is two's complement?

Why is binary used at the hardware level?

What is the largest base supported here?

What do the letters A-F mean in hex?

Why are RGB colors written as 6 hex characters?

What about octal — is it still used?

How does this calculator help web developers?

Popular Conversions

Embed this calculator on your site

More Utility Tools

Browse other categories

Premium Converters

Base Converter

Base Converter

Overview — Base Converter

From the editors — what to know before you start

Pro tips most people learn the hard way

?What is the Base Converter?

The Formula

Number Base Reference — Decimal, Binary, Octal & Hexadecimal

Put It in Perspective

Practical Examples

Frequently Asked Questions

Why is hexadecimal so popular in programming?

What is two's complement?

Why is binary used at the hardware level?

What is the largest base supported here?

What do the letters A-F mean in hex?

Why are RGB colors written as 6 hex characters?

What about octal — is it still used?

How does this calculator help web developers?

Popular Conversions

Embed this calculator on your site

More Utility Tools

Browse other categories