Binary to Decimal Converter

How to use

1. Enter Value — Type a binary or decimal number in either field
2. See Conversions — All number bases update in real time
3. Copy Result — Select and copy the value you need

What Is Binary?

Binary (base-2) is the most fundamental number system in computing. It uses only two symbols: 0 and 1. Every piece of data a computer processes — from text and images to video and software — is ultimately represented in binary.

This tool converts between binary, decimal (base-10), hexadecimal (base-16), and octal (base-8) in real time.

Why Binary Matters

Computers use binary because electronic circuits have two states: on (1) and off (0). Each binary digit is called a "bit." Eight bits form a "byte," which can represent values from 0 to 255 (00000000 to 11111111). All computer operations — from simple addition to complex AI — are performed through combinations of these binary operations.

Binary to Decimal Conversion

To convert binary to decimal, each bit is multiplied by 2 raised to its position (counting from 0 on the right):

• 10110: (1×16) + (0×8) + (1×4) + (1×2) + (0×1) = 22
• 11111111: 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255 (maximum value of one byte)
• 1000000000: 512 (only the highest bit is set)

Common Binary Values

8 bits (1 byte) = 0 to 255. 16 bits = 0 to 65,535. 32 bits = 0 to 4,294,967,295. 64 bits = 0 to 18,446,744,073,709,551,615. These are the standard integer sizes in most programming languages.

Binary in Everyday Computing

• File sizes: Measured in bytes (groups of 8 bits)
• IP addresses: IPv4 uses 32 bits (e.g., 192.168.1.1 = 11000000.10101000.00000001.00000001)
• Permissions: Unix file permissions use 3-bit groups (rwx = 111 = 7)
• Colors: 8 bits per channel (RGB), 24 bits total for 16.7 million colors
• Character encoding: ASCII uses 7 bits (128 characters), UTF-8 uses 1-4 bytes

Bitwise Operations

Programmers frequently work with binary using bitwise operations: AND (&), OR (|), XOR (^), NOT (~), left shift (<<), and right shift (>>). Understanding binary representation is essential for using these operations effectively in low-level programming, networking, and cryptography.

Privacy

All conversions run in your browser. No data is sent to any server.

Convert hex values with our Hex to Decimal Converter. Encode data with our Base64 Encoder.

Frequently asked questions

What is binary?

Binary (base-2) uses only two digits: 0 and 1. It's the fundamental number system used by computers, where each digit (bit) represents an on/off state in electronic circuits.

How do I convert binary to decimal?

Multiply each bit by its positional power of 2 (starting from 0 on the right) and sum the results. For example, 1101 = (1×8) + (1×4) + (0×2) + (1×1) = 13.

What's the largest number this can convert?

There's no practical limit. The tool uses BigInt for arbitrary precision, supporting binary strings of any length.

Can I enter binary with 0b prefix?

Yes. The tool automatically strips the 0b prefix if present, following JavaScript convention.

Related free tools

• Percentage Calculator — Calculate percentages: find X% of Y, percentage change, increase, and decrease.
• Age Calculator — Calculate exact age in years, months, and days from any birth date.
• BMI Calculator — Calculate Body Mass Index with metric or imperial units.
• Discount Calculator — Calculate sale prices, savings amount, and total with tax.
• Tip Calculator — Calculate tip amounts and split bills among any number of people.
• Unit Converter — Convert length, weight, temperature, volume, area, speed, and data units.
• Hex to Decimal Converter — Convert between hexadecimal, decimal, binary, and octal.
• Date Difference Calculator — Calculate days, weeks, months, and years between any two dates.
• Aspect Ratio Calculator — Calculate and scale aspect ratios with common presets.
• Number to Words — Convert numbers to their English word representation.
• Roman Numeral Converter — Convert between Roman numerals and decimal numbers.
• Scientific Calculator — Trig, logs, exponents, parentheses, π and e — evaluated safely in your browser. No eval, with history.