Binary to Decimal Converter
Digital Logic Decoder
The Bridge Between Machine Logic and Human Math
Network Analysis
Subnet masks and IP addresses are managed in binary; converting them to decimal is essential for subnetting and troubleshooting.
Status Register Decoding
In low-level programming, hardware status is often represented as bitstrings. Converting to decimal helps identify active flags.
Sensor Data Processing
Raw sensor outputs are often unformatted binary. Converting to decimal is the first step in digital signal processing.
Computer Science Core
A fundamental skill for understanding data representation, floating-point arithmetic, and computer architecture.
Understanding Foundational Base Conversion
Binary is a positional number system (Base-2), where each digit (bit) represents a power of 2. Converting binary to decimal involves summing the values of the powers of 2 for every "1" present in the string. This process is the ultimate bridge between electronic hardware logic and human-readable mathematics.
Key Takeaways
- Positional Worth: Calculations start from the right (2⁰) and double for each step to the left.
- Bit Activation: A "1" means the power of 2 is included in the sum; a "0" means it is ignored.
- Bounded Values: A standard 8-bit byte can represent decimal values ranging from 0 to 255.
Frequently Asked Questions
- Type or paste a binary number into the Binary Input box, using only 0s and 1s, such as 1101 or 101010.
- The Decimal Result updates automatically, along with the Chars, Bits, and Bytes stats.
- Use Copy to copy the decimal result to your clipboard.
- Use Swap to flip the tool into decimal-to-binary mode.
- Click Clear to reset the input and convert a new value.
Binary is a base-2 positional number system, so each digit, called a bit, represents a power of 2 based on its position, starting from 2 to the power of 0 on the far right and doubling for every position to the left. To convert a binary number to decimal, you multiply each bit by its positional power of 2 and add together the results for every position that contains a 1, ignoring positions that contain a 0. For example, the binary number 1101 equals (1 times 2 to the power of 3) plus (1 times 2 to the power of 2) plus (0 times 2 to the power of 1) plus (1 times 2 to the power of 0), which is 8 plus 4 plus 0 plus 1, giving a decimal value of 13.
Plain binary strings do not carry a sign on their own, so negative numbers are represented using a fixed bit width and a convention called two's complement. In two's complement, a leading 1 bit signals a negative value, and you find its magnitude by flipping every bit and adding one to the result. An 8-bit signed binary number can therefore represent decimal values from -128 to 127, rather than the 0 to 255 range used for unsigned binary.
A standard 8-bit unsigned byte can represent 256 distinct values, ranging from 00000000 up to 11111111, which equals decimal 255. Larger binary widths scale the same way: a 16-bit value maxes out at 65,535, and a 32-bit value maxes out at 4,294,967,295. Each additional bit doubles the number of representable values.
Binary is base-2 and uses only 0 and 1, while octal is base-8 and uses digits 0 through 7, and hexadecimal is base-16 and uses digits 0 through 9 plus letters A through F. Octal and hexadecimal exist mainly as shorthand for binary, since each octal digit maps to exactly three bits and each hex digit maps to exactly four bits, making long binary strings, like those in memory dumps or subnet masks, much easier for humans to read and write.