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Quick answer: A free binary to decimal converter (also called a binary to decimal calculator) changes a binary number to decimal, from base 2 to base 10. Paste one number or a list into the box above, press Convert to Decimal, and each group comes back as a whole number. Try it with your own binary.
Each group is read as an unsigned integer, a whole number with no sign bit, and our server converts every digit exactly, from an 8-bit byte to a 200,000 digit group.
It doesn't read negative numbers or fractions, and it prints the answer, not the steps.
How to Convert Binary to Decimal With This Tool
Any mix of spaces, tabs and new lines separates numbers, and each piece converts alone.
Enter or paste your Binary. Click the box and paste binary.
Upload File. Optional. A plain text (.txt) file lands in the box.
Convert to Decimal. Press it and the page reloads with your answer.
Read the Result card. Numbers appear on one line, in your order, with single spaces.
Save as TXT or Copy to Clipboard. The first downloads binary-to-decimal.txt, the second copies the numbers only.
Leading zeros are harmless: 00001010 is 10. A group with no spaces is one bit string, so 0100100001100101 returns 18533, not the letters He. Type a space after every 8 digits: the tool never cuts a stream into bytes.
Binary to Decimal Examples
Every binary to decimal conversion below ran through this page and matched Python.
Both methods rest on positional notation: the weight of each bit is a power of two, 2 to the power of its position.
Place values, for one byte. The rightmost digit, the least significant bit, is worth 1, not 2. Write 128, 64, 32, 16, 8, 4, 2 and 1 under 10010110 and add the values that sit under a 1: 128 + 16 + 4 + 2 = 150.
Doubling method, for anything longer. Start at 0 and read 110101 from the most significant bit to the least, doubling the total and adding each digit: 1, 3, 6, 13, 26, 53. The double and add loop needs no table.
Unsigned whole numbers. 11111111 gives 255. A signed byte reads those bits as minus 1, a value we never return, and two's complement explains why. A binary fraction is refused too.
Exact up to the 200,000 character cap. GMP (GNU Multiple Precision Arithmetic Library) does the math with arbitrary precision integers, which grow as needed. In our tests, groups of 64, 5,000 and 200,000 digits matched Python, and the last returned 60,206 digits in under a second.
Where code rounds. JavaScript's parseInt returns a Number, which rounds past 53 bits, so 64 ones comes back as 18446744073709552000. BigInt stays exact there, as does this page.
Fixing the "Input is not valid Binary" Message
The red-edged notice at top right never names the failed group. One bad group stops the run but your text stays put, so split a long list in half to find it.
Stray characters. Digits 2 to 9, letters, commas, underscores, signs, a 0b prefix or a trailing b all fail.
Dots. Swap the dot in 11000000.10101000 for a space.
Look-alike digits. Full-width 0 and 1 from some documents look right but fail.
Limits and Text File Upload
Count and size. Without an account you can convert up to 100 numbers, meaning groups between separators, and a free account raises that to 1,000. Input can run to 200,000 characters.
Upload File. Plain text (.txt), copied into the box, so what you type afterwards is what converts.
Frequently Asked Questions (FAQs) is a list of common questions and answers provided to quickly address common concerns or inquiries.
What is 10101 binary to decimal?
10101 is 21 in decimal, because the 1s sit on the places worth 16, 4 and 1: 16 + 4 + 1 is 21. The same method gives 1001 as 9 and 11011 as 27. Paste any other number into the box.
Can I convert several binary numbers at once, and how do I separate them?
Yes. Put a space, a tab or a new line between numbers. The answers come back in order on one line, and a string with no spaces counts as one number. Up to 100 numbers, or 1,000 with a free account.
Can this converter handle very long binary numbers?
Yes, up to a cap. No digit is rounded away, because the math uses arbitrary precision integers, not floats. In our tests, groups of 64, 256 and 200,000 digits matched Python. The limit is 200,000 characters, and longer input is refused.
Does it convert negative (signed) binary numbers?
No. Each group is read as an unsigned whole number, so 11111111 gives 255, where a signed byte would be minus 1, and a minus sign is refused. For signed values you need the two's complement method, which our guide covers.
How do I convert binary to decimal in Python or JavaScript?
In Python, int('1011', 2) returns 11, though current releases refuse to print a result past 4,300 digits until you call sys.set_int_max_str_digits(). JavaScript parseInt('1011', 2) also returns 11 but rounds past 53 bits, so use BigInt('0b' + bits) there. This page needs no code.
Is the binary to decimal converter free, and do I need an account?
It is free, with no sign-up or account needed to convert. A free account is optional and raises the number limit from 100 to 1,000, counting groups separated by spaces or new lines. An uploaded .txt file counts toward the same limits.
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