Number System Converter — Convert Binary, Octal, Decimal and Hexadecimal Instantly
How to Convert to Binary
What are Number Systems?
A number system is a way of representing numbers using a fixed set of digits and a base value. Computers and digital systems use multiple number systems depending on the context — binary for internal processing, hexadecimal for memory addresses and color codes, octal in legacy systems, and decimal for everyday human use.
The four most common number systems are:
- Binary (base 2) — uses only 0 and 1. Every piece of data inside a computer is stored as binary.
- Octal (base 8) — uses digits 0 through 7. Used in Unix file permissions and legacy computing systems.
- Decimal (base 10) — uses digits 0 through 9. The standard system used in everyday arithmetic.
- Hexadecimal (base 16) — uses digits 0 through 9 and letters A through F. Widely used in programming, HTML color codes, and memory addressing.
Freekito's Number System Converter converts any number between all four bases simultaneously. Type a value in any field and all other fields update instantly — no submit button required.
How to Use This Converter
- 1. Type a number into any of the four input fields — binary, octal, decimal, or hexadecimal.
- 2. All other fields update instantly as you type.
- 3. Click the copy button next to any field to copy that value to your clipboard.
- 4. To start a new conversion, clear any field or type a new number directly.
Notes:
- • Binary accepts only 0 and 1.
- • Octal accepts only digits 0 through 7.
- • Hexadecimal accepts digits 0 through 9 and letters A through F (case insensitive).
- • Entering an invalid character will highlight the field in red with an error message.
Frequently Asked Questions
How do you convert binary to decimal?
To convert binary to decimal, multiply each digit by 2 raised to its position power, then add all results. For example, binary 1101 equals (1×8) + (1×4) + (0×2) + (1×1) = 13 in decimal. Freekito's converter does this instantly as you type.
How do you convert decimal to hexadecimal?
To convert decimal to hexadecimal, repeatedly divide the number by 16 and record the remainders. Remainders 10 through 15 are written as A through F. For example, decimal 255 divided by 16 gives remainder 15 (F) twice, so the result is FF. Freekito calculates this automatically.
What is the difference between binary and hexadecimal?
Binary (base 2) represents numbers using only 0 and 1, requiring many digits for large values. Hexadecimal (base 16) is a compact alternative — one hex digit represents exactly 4 binary digits (bits). Programmers use hex because it is far shorter to write than binary while still mapping directly to how computers store data.
Why do computers use binary?
Computers use binary because electronic circuits have two reliable states — on (1) and off (0). These two states map directly to binary digits, making binary the most stable and efficient system for digital hardware. All other number systems are used by humans to interpret and work with binary data more easily.
What is hexadecimal used for in programming?
Hexadecimal is used in programming for memory addresses, color codes in HTML and CSS (such as #FF5733), byte values, and bitwise operations. It is preferred because one hex digit represents exactly 4 bits, making it a compact and readable way to express binary data without losing the direct relationship to how the computer stores information.
How do you convert octal to binary?
To convert octal to binary, replace each octal digit with its 3-digit binary equivalent. For example, octal 7 becomes binary 111, and octal 5 becomes binary 101. So octal 57 becomes binary 101111. Freekito converts between all bases including octal and binary directly.
Is the Number System Converter free?
Yes. Freekito's Number System Converter is completely free with no account required. All conversions happen instantly in your browser with no data sent to any server.
What is the largest number the converter supports?
The converter supports integers up to 2^53 − 1 (9,007,199,254,740,991 in decimal), which is the maximum safe integer in JavaScript. Numbers beyond this limit may lose precision. For most practical uses in programming and study, this limit will not be reached.