Binary Converter
Binary ⇄ decimal · hex · octal · text
How to Use
- 1Choose what you are converting from: binary, decimal, hex, octal or plain text.
- 2Type or paste the value. Spaces in binary are fine (1101 0110).
- 3Results for every base appear instantly as you type.
- 4Open the steps box to see exactly how the conversion works.
Binary Basics
- Place valuesbit n is worth 2ⁿ
- Binary → decimaladd up the set bits
- Decimal → binaryrepeated ÷ 2, read remainders up
- Hex shortcut1 hex digit = 4 bits
Quick Examples
Tap an example to load it above.
Everything about the Binary Converter
How base 2 works and how to convert it to decimal, hex and text by hand.
Binary is the base-2 number system computers use, where every value is written with just the digits 0 and 1. This binary converter turns binary into decimal, hexadecimal, octal and text (and back) instantly, and shows the step-by-step working so you can learn the method, not just the answer.
Each binary digit (a bit) is a power of two. Reading 11010110 from the right, the set bits are worth 2, 4, 16, 64 and 128, and adding them gives 214. That single idea powers every conversion on this page.
Shortcut: one hexadecimal digit is exactly four bits. Split 11010110 into 1101 0110, convert each nibble (13 and 6) and you get D6, with no long division needed.
Binary to decimal
Multiply each bit by its place value and add: 11010110 = 128 + 64 + 16 + 4 + 2 = 214. The rightmost bit is 2⁰ = 1, then 2¹ = 2, 2² = 4 and so on.
Decimal to binary
Divide by 2 repeatedly and collect the remainders from bottom to top: 214 ÷ 2 = 107 r 0, 107 ÷ 2 = 53 r 1, 53 ÷ 2 = 26 r 1, 26 ÷ 2 = 13 r 0, 13 ÷ 2 = 6 r 1, 6 ÷ 2 = 3 r 0, 3 ÷ 2 = 1 r 1, 1 ÷ 2 = 0 r 1 → 11010110.
Where binary shows up
- 1Programming & debugging
Bit flags, permissions (chmod 755), masks and low-level protocols are all easier to read in binary or hex.
- 2Networking
IP addresses and subnet masks are 32-bit binary numbers, so subnetting is pure binary arithmetic.
- 3Text encoding
Every character has a code, so "H" is 72, which is 01001000 in binary. The text mode converts whole words at once.
- 4Exams & homework
Computer science courses test base conversion constantly, and the steps box shows the exact working teachers expect.
Frequently Asked Questions
How do I convert binary to decimal?
Multiply each bit by its place value (1, 2, 4, 8, 16… from the right) and add the results. Example: 1011 = 8 + 0 + 2 + 1 = 11. This converter shows that expansion automatically in the steps box.
How do I convert decimal to binary?
Divide the number by 2 repeatedly and write down each remainder. When you reach 0, read the remainders from bottom to top. Example: 13 → 13÷2=6 r1, 6÷2=3 r0, 3÷2=1 r1, 1÷2=0 r1 → 1101.
How do binary and hexadecimal relate?
One hex digit equals exactly four binary digits (a nibble). Split the binary number into groups of 4 from the right and convert each group: 1101 0110 → D6. That is why programmers prefer hex, because it is compact binary.
How does binary to text work?
Each character has a numeric code (ASCII/Unicode). "H" is 72 = 01001000 and "i" is 105 = 01101001, so "Hi" is 01001000 01101001. Enter text mode and the converter encodes every character for you.
Is there a size limit on the numbers?
No practical one. The converter uses exact big-integer arithmetic, so a 100-digit binary number converts without any rounding errors, unlike calculators that lose precision after 2⁵³.
Is this binary converter free and does it work on mobile?
Yes. It is 100% free, needs no sign-up and no download. It works in any modern browser and is fully responsive. Everything runs locally in your browser; nothing is uploaded or stored.