Base converter
Convert numbers between binary, octal, decimal and hexadecimal. Type in any field and all others update instantly.
Number bases explained
A number base or radix defines how many unique digits a number system uses. Decimal uses ten digits (0–9) and is the system humans use every day. Binary uses two digits (0 and 1) and is the native language of computers. Octal uses eight digits (0–7) and was historically used in computing as a shorthand for binary. Hexadecimal uses sixteen digits (0–9 plus A–F) and is widely used in programming for its compact representation of binary data.
Why programmers use hexadecimal
Every hexadecimal digit represents exactly four binary bits. This makes hex a natural shorthand for binary — the eight-bit byte 11111111 becomes simply FF in hex, and 10110100 becomes B4. Web colors use hex — #FF5733 is a shade of orange. Memory addresses in low-level programming are written in hex. CPU registers, network packet data, and file format specifications all use hexadecimal because it is far more compact than binary while maintaining a direct relationship with the underlying bit patterns.
Binary and computer science
Binary is fundamental to how all digital computers work. Every piece of data — text, images, audio, video, programs — is ultimately stored as a sequence of 0s and 1s. A single binary digit is a bit. Eight bits make a byte, which can represent 256 different values (0 through 255). Understanding binary is essential for computer science, networking, cryptography, and low-level programming. The bit breakdown section on this tool shows exactly which bits are set for any number you enter.
Octal and Unix permissions
Octal is still actively used in Unix and Linux systems for file permissions. The chmod command uses octal notation — chmod 755 grants read, write, execute to the owner and read, execute to group and others. Each permission triplet (read, write, execute) maps perfectly to three binary bits, and three bits is exactly one octal digit. So 7 in octal is 111 in binary meaning all three permissions granted, and 5 is 101 meaning read and execute but not write.
Frequently asked questions
How do I convert decimal to binary?
Type your decimal number into the Decimal field and the binary equivalent appears instantly. For example 255 in decimal is 11111111 in binary.
What is hexadecimal?
A base-16 number system using digits 0-9 and letters A-F. Each hex digit represents exactly four binary bits. Widely used in programming, web colors, and memory addresses.
What is 255 in hexadecimal?
255 in hex is FF. In binary it is 11111111. In octal it is 377. It is the maximum value of a single byte.
What is binary?
A base-2 number system using only 0 and 1. The fundamental language of computers because digital circuits naturally represent two states — on and off.
What is octal?
A base-8 number system using digits 0-7. Each octal digit represents exactly three binary bits. Still used in Unix and Linux file permissions.