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HomemathBinary Converter

Binary Converter

Convert between binary, decimal, octal, and hexadecimal number systems instantly.

Our free Binary Converter lets you convert between binary, decimal, octal, and hexadecimal number systems instantly. It is built for students, teachers, engineers, and professionals who need fast, reliable math results who need fast, reliable results without installing software or creating an account.

Binary Converter runs entirely in your browser on CalculatorsPlus — enter your values, get instant results, and copy or share your output in one click. Your data never leaves your device; we do not store inputs on any server.

Use the binary converter to verify manual work, explore "what if" scenarios, and save time on repetitive calculations. For learning, try solving the problem by hand first, then check your answer here.

Results update in real time as you change inputs, so you can explore "what if" scenarios — adjust one variable at a time to see how it affects the outcome before committing to a purchase, plan, or decision.

This page includes step-by-step instructions, frequently asked questions, and practical tips below the calculator. Bookmark it for repeat use — many math tasks come up weekly during projects, studies, or financial planning.

Common Uses

  • Homework verification and exam preparation
  • Quick checks during work, shopping, or DIY projects
  • Teaching demonstrations and classroom examples
  • Engineering and spreadsheet formula validation

How to Use the Binary Converter

  1. 1

    Enter a number

    Input a number in decimal, binary (prefix 0b), hex (prefix 0x), or octal (prefix 0o).

  2. 2

    View all conversions

    See the number represented in all four number systems simultaneously.

💡 Tips & Tricks

  • Hex is widely used in web colors (#FF0000 = red), memory addresses, and MAC addresses.
  • Each hex digit maps to exactly 4 binary bits, making conversion easy.
  • Learn powers of 2: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024.

Frequently Asked Questions

What is binary?
Binary is a base-2 number system using only 0 and 1. It is the fundamental language of computers, where each digit (bit) represents an on/off state.
How do I convert decimal to binary?
Repeatedly divide by 2 and record remainders. Read remainders bottom to top. Example: 13 → 13/2=6r1, 6/2=3r0, 3/2=1r1, 1/2=0r1 → 1101 in binary.
What is hexadecimal?
Hexadecimal (hex) is base-16, using digits 0–9 and letters A–F (10–15). It is a compact way to represent binary: each hex digit = 4 binary bits. Example: FF = 11111111 = 255.
How do I convert binary to decimal?
Multiply each bit by 2^(position from right, starting at 0) and sum. Example: 1101 = 1×8 + 1×4 + 0×2 + 1×1 = 13.