Last updated: April 2026
The Decimal to Binary Converter transforms any decimal number into its binary equivalent along with octal and hexadecimal representations. Enter a decimal value and instantly see the binary output formatted in neat 4-bit groups for easy reading. The tool also shows how many bits are needed to represent your number, which is useful for understanding data types and memory allocation in programming. Whether you are a computer science student working through number system homework, a developer debugging bit flags, or an electronics hobbyist working with microcontrollers, this converter makes number base translation effortless. It works bidirectionally too, so you can type in binary and get the decimal back.
Type any non-negative whole number in the Decimal Number field. The binary equivalent generates instantly as you type.
If you have a binary value, type it in the Binary Number field instead. The decimal and other number base representations update automatically.
The main result shows your binary number with digits grouped into sets of four (nibbles) for easy reading. Below that, you will find decimal, binary, octal, and hexadecimal values all displayed together.
Click the copy button next to any number format to grab it for your code, documentation, or homework.
Decimal to Binary Converter is the fastest way to convert numbers between bases online. Key advantages include 4-bit grouped display, multi-base output, bit count display, and bidirectional conversion.
Divide the decimal number by 2 repeatedly, recording the remainder each time. Read the remainders from bottom to top to get the binary representation. For example, decimal 13: 13 / 2 = 6 remainder 1, 6 / 2 = 3 remainder 0, 3 / 2 = 1 remainder 1, 1 / 2 = 0 remainder 1. Reading bottom to top: 1101 in binary.
A 4-bit group (also called a nibble) contains four binary digits. Grouping binary numbers into nibbles makes them much easier to read and directly corresponds to one hexadecimal digit. For example, 11111111 is hard to read, but 1111 1111 clearly shows two groups that each equal F in hex, giving FF.
The number of bits needed equals the position of the highest set bit plus one. For decimal 255, you need 8 bits (11111111). For decimal 256, you need 9 bits (100000000). This tool shows the bit count automatically, which is helpful when choosing data types in programming (8-bit byte, 16-bit short, 32-bit int, 64-bit long).
This tool works with non-negative integers (0 and positive whole numbers). Negative numbers in binary require a representation scheme like two's complement, which depends on the specific bit width (8-bit, 16-bit, 32-bit, etc.). For negative number conversions, you would need to specify the bit width and apply two's complement rules.
All three are positional number systems used in computing. Binary (base 2) is the most fundamental. Octal (base 8) groups binary into 3-bit chunks, so each octal digit equals three binary digits. Hexadecimal (base 16) groups binary into 4-bit chunks, so each hex digit equals four binary digits. This is why programmers commonly use hex as a shorter way to write binary values.