How to Convert Binary to Decimal (Two Easy Methods)

To convert binary to decimal, assign each digit a place value starting at 1 on the right and doubling as you move left (1, 2, 4, 8, 16…), then add up the place values wherever the binary digit is 1. For example, 1101 has 1s in the eights, fours, and ones places: 8 + 4 + 1 = 13.

Two methods get you there. The place-value method is easier to understand; the doubling method is faster once you’re comfortable. Both below, with worked examples.

Method 1: Place values

This is the method to learn first, because it shows you why the answer is what it is.

1. Write out the binary number.
2. Under each digit, write its place value. Start at the rightmost digit with 1, then double for each step left: 1, 2, 4, 8, 16, 32, 64, 128.
3. Cross out every place value sitting under a 0. Those contribute nothing.
4. Add up the place values sitting under a 1. The sum is your decimal number.

Worked example with 1101. It has four digits, so the place values from left to right are 8, 4, 2, 1. The digits are on, on, off, on. Cross out the 2. Add the rest: 8 + 4 + 1 = 13. Done.

One more, slightly longer: 10100. Five digits, so places 16, 8, 4, 2, 1. Only the sixteens place and the fours place hold a 1. 16 + 4 = 20.

Where this goes wrong for most people: labeling place values left to right. The 1s place is always on the right, because that’s the side where new digits don’t change existing ones. If your answer comes out weirdly large or small, this is almost always why. The other classic slip is adding values under the 0s. A zero means “skip me,” every time.

Method 2: Doubling (faster, no place values needed)

The doubling method (sometimes taught as the Horner scheme) reads the number left to right and never writes a place value at all.

1. Start with a running total of 0.
2. Read the binary digits left to right. For each digit: double your running total, then add the digit.
3. When you run out of digits, the running total is the answer.

Same example, 1101, digits read left to right: 1, 1, 0, 1.

• Start at 0. Double it (still 0), add the first digit: total 1.
• Double (2), add the next digit: total 3.
• Double (6), add 0: total 6.
• Double (12), add the last digit: total 13.

Answer: 13, matching Method 1.

And 10100, digits 1, 0, 1, 0, 0: totals run 1, then 2, then 5, then 10, then 20.

Why bother with a second method? Length. For a byte-sized number the place-value method means keeping eight place values straight. Doubling just needs you to multiply by 2 and occasionally add 1, which you can do in your head while reading the digits once. It’s also the method that generalizes: replace “double” with “multiply by 8” and you’re converting octal.

The catch: doubling gives you no partial picture. Mess up one step and the error silently compounds. When accuracy matters more than speed, use place values, or run both and compare.

Checking your work

Fast sanity checks that catch most mistakes:

• Parity. If the binary number ends in 1, the decimal answer must be odd. Ends in 0, must be even. This one check catches roughly half of all arithmetic slips.
• Range. A binary number with five digits can’t exceed 31, and one with eight digits can’t exceed 255. If your five-digit conversion says 40, a place value got doubled wrong.
• Reverse it. Convert your answer back with the decimal to binary method and see if you land on the original digits.

Or check against the binary to decimal converter, which is instant and shows its work. Using the tool to verify hand conversions is honestly the fastest way to get good at this.

Where you’ll use this

Binary-to-decimal is the workhorse conversion behind almost everything else in this corner of math. Decoding binary text runs through it (each byte becomes a decimal number before it becomes a letter, as shown in how to read binary). Networking classes use it for subnet masks. Electronics projects use it for reading registers. And if you just want to build number sense, scanning the numbers in binary table until the patterns feel familiar works better than it has any right to.

For arithmetic in base 2 itself, addition and multiplication without converting back and forth, the binary calculator has you covered. And if the “why” behind place values is still fuzzy, the binary number system article builds it from the ground up.

FAQ

How do you convert binary to decimal by hand?

Label each binary digit with a place value, starting at 1 on the right and doubling leftward. Then add the place values wherever the digit is 1. For 1101, the places are 8, 4, 2, 1, and the 1s sit over 8, 4, and 1, so the answer is 13.

What is the doubling method for binary?

Read the binary number left to right, keeping a running total that starts at 0. At each digit, double the total and add that digit. After the last digit, the total is the decimal value. It’s quick for long numbers because you never track place values explicitly.

What is 1101 in decimal?

It’s 13. The eights, fours, and ones places contain 1s, and 8 + 4 + 1 = 13. You can confirm with the doubling method: reading left to right, the running total goes 1, 3, 6, 13. Both methods always agree when done correctly.

How do I know if my conversion is right?

Check parity first: a binary number ending in 1 must convert to an odd decimal number, and one ending in 0 must be even. Then check range: n binary digits can’t exceed one less than 2 to the n. For certainty, convert the answer back to binary or use the binary to decimal tool.

Do I need to convert binary to read binary text?

Yes, it’s the middle step. Text decoding splits the binary into 8-bit bytes, converts each byte to decimal exactly as described here, then looks the number up in an ASCII table to find the character. The conversion methods on this page power that second step.