How to Convert Binary to Decimal: Step-by-Step Guide

To convert binary to decimal, multiply each bit by its power of two (starting at 2⁰ on the right) and add the results, or paste your 0s and 1s into a binary to decimal converter to get the exact base-10 value instantly. Binary is base-2, so each position is worth double the one to its right. This guide walks you through the manual method and the one-click online way.

The idea behind base 2 to base 10

A binary number is just a sum of powers of two. Reading from the right, each digit sits over a place value of 1, 2, 4, 8, 16, 32 and so on. Wherever there is a 1, you count that place value; wherever there is a 0, you skip it. Add the counted values together and you have the decimal number. That is the whole rule, whether the string is four bits or four hundred.

Convert binary to decimal by hand

Take the binary number 10110 as an example. Line up each bit with its place value from right to left:

Bit	1	0	1	1	0
Place value	16	8	4	2	1
Counts?	Yes	No	Yes	Yes	No

Add the place values under every 1: 16 + 4 + 2 = 22. So 10110 in binary equals 22 in decimal. The same steps work for any length; you just keep doubling the place value for each column you move left.

Convert binary to decimal online in four steps

Doing it by hand is great for learning, but for long strings a converter is faster and error-proof. Here is how to use the ByteTools converter:

1. Type or paste your binary string (only 0s and 1s) into the input box.
2. Leave any spaces or line breaks in place — grouped binary like 1011 0110 is handled automatically.
3. Read the decimal result, which updates instantly as you type.
4. Click once to copy the decimal value wherever you need it.

If you accidentally include a character that is not a 0 or 1, the tool flags it with a clear error instead of returning a silently wrong number, so a stray letter or a pasted comma never slips through.

Why big numbers convert exactly

Long binary strings — 64-bit register dumps, hashes, permission masks — overflow the precision of ordinary floating-point math, which quietly rounds the result. The ByteTools converter uses JavaScript's BigInt, so even a 128-bit binary value converts to its exact decimal equivalent with zero rounding. That accuracy is the main reason to reach for a dedicated tool rather than a quick calculator when the numbers get large.

Private and offline by design

Every calculation happens locally in your browser. Nothing you paste is uploaded, logged or stored, which matters when the binary encodes sensitive data. Because it is a client-side tool, it also keeps working after the page has loaded even if you lose your connection.

Try the Binary to Decimal converter — free and 100% in your browser.

FAQ

Do I read binary left to right or right to left?

For place values, read right to left: the rightmost bit is the ones place (2⁰) and each step left doubles the value. The written order of the digits stays the same — you just assign the smallest place value to the last digit.

How do I convert a signed or negative binary number?

This converter treats the input as an unsigned binary value, so it reads every bit as a positive place value. If your data uses two's-complement to represent negatives, convert the magnitude and apply the sign separately based on the leading bit.

Is there a limit on how many bits I can convert?

No practical limit. Because the tool uses BigInt, you can convert strings far longer than 64 bits and still get an exact decimal figure without overflow or rounding.

Why did my conversion show an error?

The input contained a character other than 0 or 1 — often a letter, a stray comma or a hidden character from a copy-paste. Remove the offending character and the decimal value appears again. Spaces and line breaks are fine and are ignored automatically.

Related free tools

• Decimal to Binary — go the other way, from base 10 back to bits.
• Hex to Decimal — convert hexadecimal values to base 10.
• Decimal to Hex — turn decimal numbers into hexadecimal.
• Binary Calculator — add, subtract and operate on binary numbers directly.

Built by ByteVancer

ByteTools is a free product of ByteVancer, a software and web development studio that builds web apps, SaaS platforms and custom software. If you need a reliable engineering partner beyond these free utilities, explore what ByteVancer can build for your team.