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Number System Converter Free - Binary Hex Octal Online

Free online number system converter to convert between binary, decimal, octal, and hexadecimal instantly. Copy any format with one click - no login, no signup.

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About this tool

Binary, decimal, hex, and octal appear constantly in computer science - from memory addresses and color codes to bitmasking and register values. Converting mentally between them is error-prone; a calculator gives you the correct value immediately.

Convert instantly between binary (base 2), decimal (base 10), hexadecimal (base 16), and octal (base 8). Enter a value in any base and see the equivalent in all four formats simultaneously.

How to Use Number System Converter

Enter a Number

Type a number in binary, decimal, octal, or hexadecimal.

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Auto Convert

All other formats update instantly as you type.

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Copy Any Format

Click copy next to binary, decimal, octal, or hex to grab the value.

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Try Another

Clear and enter a new number in any base to convert again.

Common Workflows

CS Coursework

Convert binary to decimal for CS coursework and assignments.

Hex Color Codes

Convert hex color codes to decimal RGB values.

Bitmasking & Flags

Convert decimal to binary for bitmasking and flag operations.

Unix Permissions

Convert octal to binary for Unix file permissions.

Memory Address Debugging

Debug memory addresses shown in hexadecimal.

Exam Practice

Practice number system conversions for CS exams.

Best For

Converts between all four number systems simultaneously - change one, all others update instantly.
Supports hexadecimal input with A–F notation; no manual case conversion needed.
Useful for CS coursework, embedded systems programming, and low-level debugging.

Examples

Converting binary to decimal by hand (positional notation)

Binary

Manual Calculation

1×32 + 0×16 + 1×8 + 0×4 + 1×2 + 0×1 = 32 + 8 + 2 = 42

Each binary digit represents a power of 2, counting from the right (2⁰, 2¹, 2², ...). Add up the powers of 2 where the digit is 1 to get the decimal value - this tool shows the same answer (42) instantly in the Decimal field.

Converting decimal to binary by hand (divide-by-2 method)

Decimal

Manual Calculation

42÷2=21 r0 · 21÷2=10 r1 · 10÷2=5 r0 · 5÷2=2 r1 · 2÷2=1 r0 · 1÷2=0 r1 → read remainders bottom to top: 101010

Divide by 2 repeatedly, tracking the remainder each time, until you reach 0. Reading the remainders from last to first gives the binary value - this tool's Binary field shows the same result (101010) instantly.

Reading the Bit Info panel

Decimal

Bit Info

Decimal: 256 · Bits needed: 9 · Bytes: 2

The Bit Info panel shows the minimum number of bits needed to represent the current decimal value, and how many bytes that rounds up to. 8 bits can only represent up to 255 (2^8 - 1), so 256 needs a 9th bit - which rounds up to 2 bytes.

Use Cases

Checking a hand-worked homework answer

Convert a binary or hex value here to verify an answer calculated manually for a CS assignment or exam.

Reading a hexadecimal memory address or color code

Paste a hex value from a debugger, stack trace, or CSS hex color to see its decimal equivalent instantly, without doing the base-16 math by hand.

Working out Unix file permission values

Convert an octal permission value like 755 to binary to see exactly which read/write/execute bits are set for owner, group, and others.

Sizing a value for a fixed-width data type

Enter a decimal value and check the Bit Info panel to see the minimum bits and bytes it needs, before choosing an integer type in code.

Common Mistakes

Problem

Typing a prefix like 0x or 0b into the field

Solution

The tool strips a leading 0b, 0o, or 0x automatically if you type one, but entering the raw digits directly (e.g. FF instead of 0xFF) is what each field expects.

Problem

Expecting negative numbers or decimals to convert

Solution

Every field only accepts non-negative whole numbers - there's no minus sign or decimal point support, so fractional values and negative numbers aren't handled.

Problem

Clearing one field and expecting the others to keep their value

Solution

Emptying any single field resets all four fields to blank, since they're all derived from one shared decimal value - there's no way to clear just one.

Problem

Typing digits that don't belong to the selected base

Solution

Each field only accepts its own valid digits (0-1 for binary, 0-7 for octal, 0-9 for decimal, 0-9/A-F for hex) - invalid characters are simply not entered rather than flagged with an error message.

Tips & Best Practices

Use the Quick Examples to see common values at a glance

The four preset buttons (255/FF, 42, 256, 1024) fill all four fields instantly - useful reference points for spotting patterns like 255 = FF or 1024 being a power of 2.

Check Bit Info before choosing an integer type

The Bits needed and Bytes figures update live as you type - a quick way to confirm whether a value fits in an 8-bit, 16-bit, or 32-bit field before writing code around it.

Work the method by hand first, then check it here

Convert your own hand-worked answer here - if the tool's result doesn't match what you calculated, you'll immediately know which conversion needs another look.

Limitations

No negative numbers or fractional values

Only non-negative whole numbers are supported - there's no way to convert a negative integer (such as via two's complement) or a value with a decimal point.

No step-by-step conversion display

The tool shows the converted result instantly, not the intermediate arithmetic like a divide-by-2 ladder or positional-notation breakdown - see the Examples above for how to work through the method by hand.

Four bases only

Binary, octal, decimal, and hexadecimal are supported - there's no built-in option for other bases like base 32 or base 64.

No bulk or batch conversion

The tool converts one value at a time - there's no way to paste a list of numbers and convert them all at once.

Comparisons

Binary vs Hexadecimal

Both represent the same underlying value, but hex is far more compact - each hex digit stands in for exactly 4 binary digits, which is why programmers read memory addresses and color codes in hex instead of binary.

	Binary	Hexadecimal
Digits used	0-1	0-9, A-F
Digits needed for the value 255	8 digits - 11111111	2 digits - FF
Typical use	Bit-level operations, flags, low-level logic	Memory addresses, color codes, compact display of binary data

Which should you use?

Hex is really just a shorthand for binary - every hex digit maps to exactly 4 binary digits (a nibble), which is why converting between the two is regrouping rather than real math. Decimal and octal represent the same underlying value, just with different groupings.

FAQs

The most common questions are how to convert binary to decimal by hand, and why computers use binary in the first place. The Examples below walk through the manual method step by step - the short answer on binary itself: transistors have two states (on/off), which maps directly to 1 and 0.

Which number systems does this converter support?

It converts between binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16) - the four systems used most in computing and programming.