Binary to Decimal / Decimal to Binary

Binary to Decimal / Decimal to Binary

Convert base-2 binary strings to base-10 decimal integers locally in your web browser. Built on client-side arithmetic engines, this tool processes conversions directly in sandbox memory, ensuring that IP address bytes or file permission parameters are never sent to external servers.

Manual Conversion Calculations & Worked Example

Binary numbers use base-2 positional notation, where each digit (bit) represents a power of 2:

1. 1Positional Weighting:

Each column in a binary number has a weight starting from the rightmost bit (least significant bit, LSB) moving left:

• 1st column (right): 2^0 = 1
• 2nd column: 2^1 = 2
• 3rd column: 2^2 = 4
• 4th column: 2^3 = 8
• 5th column: 2^4 = 16, and so on.

1. 2The Summation Formula:

To convert a binary number to decimal, multiply each bit (d_k) by its corresponding positional weight (2^k) and calculate the sum:

Decimal = sum(from k=0 to n-1) (d_k * 2^k)

Where d_k is the bit value (0 or 1) at index k (counting from 0 on the right).

1. 3IP Octet Example Conversion (Binary 11000000):
2. 2Bit index 6: 1 * 2^6 = 64
3. 3Bit index 7: 1 * 2^7 = 128
4. 4All other indices are 0.
5. 5Sum: 128 + 64 = 192. (This is the decimal representation of the first octet of a class C IP subnet mask).

[Input Binary String (e.g. 11000000)]
               |
               v
[Map each bit to its positional weight: 128, 64, 32, 16...]
               |
               v
[Multiply bit values by weights and calculate sum]
               |
               v
[Output Decimal Integer (192)]

• Subnet Octet: The binary octet 11111111 translates to 128+64+32+16+8+4+2+1 = 255.
• IP Prefix: The binary string 11000000 translates to 128+64 = 192.
• Byte Flag: The binary string 10101010 translates to 128+32+8+2 = 170.

Encoding & Conversion Standards

• Internet Engineering Task Force (IETF): RFC 4632 on Classless Inter-Domain Routing (CIDR).
• NIST Guide on Unit Representations: Standard representation of binary and digital parameters.
• MDN Web Docs: Math and calculation syntax reference.

Binary to Decimal Converter Online — IP Subnetting & Bit Registers

This utility performs positional notation conversions to translate binary numbers (composed of 0s and 1s) into standard human-readable decimal integers. It processes unsigned binary strings and outputs their decimal equivalence instantly.

• Output Shows NaN: This happens if you enter letters, spaces, or numbers other than 0 and 1 inside the input. Strip all non-binary characters to fix the error.
• Result Seems Too Small: Ensure you haven't omitted leading 1 bits during copy-paste.
• Results Aren't Loading: Ensure JavaScript is enabled in your browser settings.

What is standard dotted-decimal notation?

Dotted-decimal notation is the format used for IPv4 addresses, where 32-bit binary addresses are split into four 8-bit octets and converted to decimal numbers separated by dots (e.g., 192.168.1.1).

How many bits represent a standard subnet mask?

A standard IPv4 subnet mask consists of 32 bits, divided into four 8-bit segments (bytes). The number of leading 1 bits determines the subnet's network prefix length (CIDR).

Are my binary inputs logged?

No. All calculations run locally on your device within your web browser sandbox.

• Decimal to Binary: Convert decimal integers (Base 10) to binary string formats (Base 2).
• kg to lbs: Convert weight measurements from Kilograms (kg) to Pounds (lbs).
• lbs to kg: Convert weight measurements from Pounds (lbs) to Kilograms (kg).
• Celsius to Fahrenheit: Convert temperatures from Celsius (°C) to Fahrenheit (°F).
• Fahrenheit to Celsius: Convert temperatures from Fahrenheit (°F) to Celsius (°C).
• Meters to Feet: Convert length measurements from Meters (m) to Feet (ft).

Typical Manual Conversion Errors

• Including Non-Binary Characters: Attempting to convert strings that contain characters other than 0 and 1 (like 2 or letters). The parser will reject these inputs.
• Reading Left-to-Right: Calculating positional weights starting from the left instead of the right, resulting in incorrect values.
• Adding Incorrect Powers: Confusing powers of 2 (e.g., assuming 2^3 is 6 instead of 8).