Binary to Decimal Converter

What is binary to decimal conversion?

Binary is a base-2 number system that uses only two digits: 0 and 1. Decimal is a base-10 number system that uses ten digits: 0 through 9. Converting binary to decimal means translating a number written in base 2 into its equivalent value in base 10.

Every computer, phone, and digital device stores and processes data in binary — because electronic circuits have two natural states: on and off. But humans think in decimal. That's why binary-to-decimal conversion comes up everywhere: programming, networking, digital electronics, computer science homework, and even competitive exams.

For example, the binary number 1011 equals 11 in decimal. The binary number 11111111 equals 255, which is the maximum value of a single byte (8 bits). And 10000000 equals 128, the highest bit in an 8-bit unsigned integer.

How to convert binary to decimal (with examples)

The method is simple: multiply each binary digit by 2 raised to the power of its position, then add all the results together. Positions are counted from right to left, starting at 0.

Example 1: Convert 1011 to decimal

1. Rightmost bit (position 0): 1 × 2⁰ = 1 × 1 = 1
2. Next bit (position 1): 1 × 2¹ = 1 × 2 = 2
3. Next bit (position 2): 0 × 2² = 0 × 4 = 0
4. Leftmost bit (position 3): 1 × 2³ = 1 × 8 = 8
5. Add them: 8 + 0 + 2 + 1 = 11

So 1011₂ = 11₁₀.

Example 2: Convert 11001010 to decimal

1. Position 0: 0 × 1 = 0
2. Position 1: 1 × 2 = 2
3. Position 2: 0 × 4 = 0
4. Position 3: 1 × 8 = 8
5. Position 4: 0 × 16 = 0
6. Position 5: 0 × 32 = 0
7. Position 6: 1 × 64 = 64
8. Position 7: 1 × 128 = 128
9. Sum: 128 + 64 + 8 + 2 = 202

So 11001010₂ = 202₁₀.

The tool above does all of this automatically and shows you the full breakdown, so you can check your work or learn the process step by step.

Why use this binary to decimal converter?

Quick reference: binary to decimal chart

Here are the most common binary-to-decimal conversions. This table is handy for quick lookups or study sessions.

For a larger range, just paste any binary number into the tool above. It handles everything from single bits to thousand-bit strings.

When would you need to convert binary to decimal?

Computer science and programming

• Debugging low-level code that manipulates bit flags, bitmasks, or hardware registers
• Understanding memory addresses, permission bits (like Unix file modes), or network masks
• Working with binary protocols, file formats, or serialized data
• Converting binary literals in code (e.g., 0b1011) to their decimal equivalents for verification

Students and exams

• Homework and assignments in digital electronics, computer architecture, or discrete math
• Competitive exams that include number system questions
• Practicing conversions by checking your answers against the step-by-step breakdown

Networking and IT

• Converting subnet masks from binary to dotted-decimal notation
• Understanding IPv4 address calculations and CIDR notation
• Working with MAC addresses, binary headers, or protocol flags

Everyday curiosity

• Figuring out what a binary string represents — maybe you saw it in a puzzle, a game, or a meme
• Checking what 11111111 or 10101010 actually equals
• Teaching someone how binary numbers work with a live example

Binary vs decimal vs hexadecimal

Binary is base 2, decimal is base 10, and hexadecimal is base 16. Programmers often use all three, sometimes in the same file. Here's how they compare:

Binary is the most fundamental, hexadecimal is the most compact, and decimal is the most human-readable. This tool focuses on binary ↔ decimal, which is the most common conversion for learning and debugging.

Frequently asked questions