Binary Converter
Convert between binary, decimal, hexadecimal, and octal instantly. See step-by-step conversions with power-of-two and place value breakdowns. Perfect for computer science students, developers, and IT professionals.
What Is a Binary Converter?
A binary converter is a tool that converts numbers between different number systems (also called bases). The four most common systems are:
- Binary (Base 2): Uses only 0 and 1. The foundation of all digital computing.
- Decimal (Base 10): Uses 0-9. The standard system for everyday human counting.
- Hexadecimal (Base 16): Uses 0-9 and A-F. Compact representation of binary data.
- Octal (Base 8): Uses 0-7. Historical system used in some computing contexts.
This converter shows you not just the result, but also the step-by-step process for each conversion, making it a valuable learning tool for computer science students and developers.
How Does the Binary Converter Work?
The converter uses standard base conversion algorithms:
Binary → Decimal:
Multiply each bit by its place value (power of 2) and sum the results.
Example: 1010₂ = 1×2³ + 0×2² + 1×2¹ + 0×2⁰ = 8 + 0 + 2 + 0 = 10₁₀
Decimal → Binary:
Repeatedly divide by 2, recording the remainders. Read remainders in reverse order.
Example: 10₁₀ → 10÷2=5 (r0), 5÷2=2 (r1), 2÷2=1 (r0), 1÷2=0 (r1) → 1010₂
Binary ↔ Hexadecimal:
Group binary digits in sets of 4 (nibbles). Each nibble maps to one hex digit.
Example: 1010 1010₂ → AA₁₆
Binary ↔ Octal:
Group binary digits in sets of 3. Each group maps to one octal digit.
Example: 010 101 010₂ → 252₈
Why Use This Binary Converter?
- Four Systems: Convert between binary, decimal, hexadecimal, and octal.
- Step-by-Step: See exactly how each conversion is calculated.
- Visual Breakdown: A bar chart shows the place values of binary digits.
- Educational: Perfect for learning number systems and base conversion.
- Free & Private: No registration, no data storage.
Common Uses for Binary Conversion
- Computer Science Education: Learning how computers represent and process numbers.
- Programming: Working with bitwise operations, memory addresses, and data encoding.
- Digital Electronics: Understanding how binary signals represent information.
- Network Engineering: Converting IP addresses, subnet masks, and CIDR notation.
- Cryptography: Working with binary data in encryption algorithms.
❓ Binary Converter FAQ
What is binary?
Binary is a base-2 number system that uses only two digits: 0 and 1. It is the fundamental language of computers, where each digit (bit) represents an on/off state.
How do I convert binary to decimal?
Multiply each binary digit by its place value (power of 2) and add the results. For example, 1010₂ = 1×8 + 0×4 + 1×2 + 0×1 = 10₁₀. This calculator shows the complete breakdown.
How do I convert decimal to binary?
Repeatedly divide the decimal number by 2, recording the remainders. Read the remainders from last to first. For example, 10₁₀ = 1010₂. The calculator displays each step.
What is hexadecimal?
Hexadecimal is a base-16 number system that uses digits 0-9 and letters A-F (where A=10, B=11, C=12, D=13, E=14, F=15). It's commonly used in computing because each hex digit represents exactly 4 binary bits (a nibble).
What is octal?
Octal is a base-8 number system that uses digits 0-7. It's less common today but was historically used in computing because each octal digit represents exactly 3 binary bits.
How do I convert binary to hexadecimal?
Group binary digits into sets of 4, starting from the right. Convert each 4-bit group to its hexadecimal equivalent. For example, 10101010₂ = 1010 1010₂ = AA₁₆.
How do I convert binary to octal?
Group binary digits into sets of 3, starting from the right. Convert each 3-bit group to its octal equivalent. For example, 10101010₂ = 010 101 010₂ = 252₈.
How do I convert hexadecimal to binary?
Convert each hex digit to its 4-bit binary equivalent. For example, AA₁₆ = 1010 1010₂ = 10101010₂.
How do I convert octal to binary?
Convert each octal digit to its 3-bit binary equivalent. For example, 252₈ = 010 101 010₂ = 10101010₂.
What is a bit?
A bit (binary digit) is the smallest unit of data in computing, representing either 0 or 1. A group of 8 bits is called a byte.
What is a nibble?
A nibble is a group of 4 binary bits. It can represent 16 different values (0-15) and corresponds to a single hexadecimal digit.
Why do computers use binary?
Computers use binary because electronic circuits can reliably distinguish between two states: on (1) and off (0). This binary foundation makes computers simple, reliable, and fast.
What is the difference between binary and decimal?
Binary uses base 2 (digits 0-1), while decimal uses base 10 (digits 0-9). Binary is used by computers internally; decimal is the human-friendly system used in everyday life.
What is the largest number a byte can represent?
A byte (8 bits) can represent values from 0 to 255 in decimal, or 00 to FF in hexadecimal. The maximum binary value is 11111111₂.
How do I convert a negative number to binary?
Negative numbers are typically represented using two's complement notation. This calculator handles positive integers only. For negative numbers, use a dedicated two's complement calculator.
What is the binary representation of the decimal number 255?
255₁₀ = 11111111₂ (eight 1s). This is the maximum value of a single byte.
What is the hexadecimal representation of the decimal number 255?
255₁₀ = FF₁₆. Each F represents 15, so FF = 15×16 + 15 = 255.
How do I use this converter for IP addresses?
IP addresses are often represented in decimal (e.g., 192.168.1.1) but are binary underneath. Use this converter to see the binary representation of each octet of an IP address.