Binary to Decimal Converter
Translate a base-2 binary value into a base-10 decimal number.
Interactive visual
See binary place values add up
101101 → 45
Live input
101101
Live output
Updates as you type
Convert binary into decimal
Example: 101101 → 45
Decimal result
Provide input
Validate format
Return decimal result
How Binary-to-Decimal Conversion Works
The Binary Number System
The binary number system, also known as base-2, uses only two digits, 0 and 1, to represent all values. Each digit position in a binary number represents a power of two, starting from 1 on the far right and doubling with each position to the left: 1, 2, 4, 8, 16, 32, 64, and so on.
Step-by-Step Conversion Method
To convert a binary number to decimal, multiply each bit by its corresponding power of two, then add all the results together. For example, the binary number 101101 is calculated as: (1 times 32) + (0 times 16) + (1 times 8) + (1 times 4) + (0 times 2) + (1 times 1) = 32 + 0 + 8 + 4 + 0 + 1 = 45. This positional value approach is the foundation of how all base conversion works.
Why Binary Matters
Binary is the fundamental language of all digital computers and electronic devices. At the hardware level, computer processors use billions of tiny transistors that can be either on (1) or off (0). Every piece of data, including text, images, video, and software, is ultimately stored and processed as sequences of binary digits called bits. A group of 8 bits forms a byte, which can represent 256 different values from 0 to 255.
Practical Applications
Understanding binary-to-decimal conversion is essential in computer science, networking (IP addresses are 32-bit binary numbers), digital electronics, and programming. Network engineers use binary to calculate subnet masks, programmers use binary for bitwise operations, and embedded systems developers work directly with binary register values. This converter lets you quickly verify binary values without manual calculation.