Binary to Decimal Converter

About the Binary to Decimal Converter

The Binary to Decimal Converter converts binary (base-2) numbers to decimal (base-10), hexadecimal (base-16), and octal (base-8). Enter a string of 0s and 1s and review the converted values with a step-by-step positional breakdown showing how each bit contributes to the final number.

Binary is the native language of all computers. Every piece of data — text, images, videos, programs — is ultimately stored as binary. Understanding binary conversion is fundamental to computer science, networking, and digital electronics. Each binary digit (bit) represents a power of 2.

This converter supports binary numbers of any length and provides the equivalent value in decimal, hex, and octal for cross-referencing. The step-by-step expansion shows each bit's contribution to the total, making it a great learning tool.

When This Page Helps

Binary conversion is essential for computer science students, programmers, and network engineers. This calculator converts the value and shows the positional-notation math for educational use.

How to Use the Inputs

1. Enter a binary number (only 0s and 1s).
2. Spaces between groups of digits are allowed and will be stripped.
3. View the decimal, hexadecimal, and octal equivalents.
4. Review the positional breakdown showing each bit's value.
5. Use this to verify subnet masks, permissions, and bitwise operations.

Example Calculation

Tips & Best Practices

• Powers of 2 to memorize: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024.
• An 8-bit byte has a maximum decimal value of 255 (11111111 in binary).
• Subnet masks in networking are binary patterns: 255.255.255.0 = 24 ones followed by 8 zeros.
• Unix file permissions use 3-bit binary groups: rwx = 111 = 7 in octal.
• Group binary digits in sets of 4 from the right to quickly convert to hex.

Binary: The Language of Computers

Every computer processor executes instructions in binary. Data is stored in binary on hard drives, SSDs, and RAM. Network packets are binary. Understanding binary is not just academic — it's practical knowledge for anyone working with technology.

Common Binary Patterns

11111111 = 255 (full byte), 10000000 = 128 (high bit set), 01111111 = 127 (max signed 8-bit), 11111111 11111111 = 65,535 (full 16-bit word). These patterns appear constantly in programming and networking.

Signed vs. Unsigned Binary

Unsigned binary treats all bits as magnitude: 8 bits hold 0–255. Signed binary (two's complement) uses the high bit as a sign bit: 8 bits hold -128 to +127. Most programming uses signed integers by default.

Frequently Asked Questions

• How do I convert binary to decimal manually?

  Write the binary number and assign powers of 2 to each bit from right (2⁰=1) to left. Multiply each bit by its power of 2 and sum the results. For 1010: 1×8 + 0×4 + 1×2 + 0×1 = 10.

• What is a binary number?

  A binary number uses only two digits: 0 and 1. Each digit is called a bit. Binary is the foundation of all digital computing because electronic circuits have two states: on (1) and off (0).

• How many decimal values can 8 bits represent?

  8 bits can represent 2⁸ = 256 values, ranging from 0 (00000000) to 255 (11111111). This is why a byte (8 bits) stores values from 0 to 255.

• What is the binary equivalent of 255?

  255 in binary is 11111111 (eight 1s). This is the maximum value for an unsigned 8-bit byte: 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255.

• How do I convert binary to hexadecimal?

  Group the binary digits into sets of 4 from the right (pad with leading zeros if needed). Convert each group to its hex equivalent: 0000=0, 0001=1, ..., 1010=A, 1011=B, ..., 1111=F.

• Why is binary important in networking?

  IP addresses and subnet masks are 32-bit binary numbers. Understanding binary helps with subnetting, CIDR notation, and network address calculations. For example, a /24 subnet mask is 11111111.11111111.11111111.00000000.