How to Convert Binary to Decimal (Step by Step, With Worked Examples)
Computers speak binary — strings of 1s and 0s. We speak decimal — the everyday numbers 0 to 9. Sooner or later, if you work with computers or study them, you will need to convert a binary number into a decimal number.
The good news is that the method is simple. Once you learn it, you can convert any binary number with a pen and paper. This guide teaches you the place-value method step by step, with four worked examples you can check.
What Does “Binary to Decimal” Mean?
Binary is base 2. It uses only two digits: 0 and 1, and every position in a binary number is worth twice as much as the position to its right.
Decimal is base 10 — the counting system you use every day, where every position is worth ten times as much as the position to its right.
Converting binary to decimal means answering one question: what ordinary number does this string of 1s and 0s represent? For example, the binary number 1010 represents the decimal number 10. They are the same value, written in two different systems — like “ten” and “10” are the same number in words and digits.
The Place-Value Method in 3 Steps
Every binary digit sits on a “place value” — a power of 2. From right to left, the place values are 1, 2, 4, 8, 16, 32, 64, 128, and so on, doubling each time.
To convert any binary number to decimal:
Step 1: Write the place values (1, 2, 4, 8, 16…) under the binary digits, starting from 1 on the right.
Step 2: Multiply each binary digit (0 or 1) by the place value below it. A 1 keeps the place value; a 0 wipes it out.
Step 3: Add up all the results. The total is your decimal number.
That is the whole method. Now let us use it.
Worked Example 1: Convert 1010 to Decimal
Write the place values under the digits:
| Binary digit | 1 | 0 | 1 | 0 |
|---|---|---|---|---|
| Place value | 8 | 4 | 2 | 1 |
| Result | 8 | 0 | 2 | 0 |
Now add the results: 8 + 0 + 2 + 0 = 10.
So 1010 in binary equals 10 in decimal. Notice how the 0s contribute nothing — only the positions holding a 1 count. That is why this method is fast: you only need to add the place values where you see a 1.
Worked Example 2: Convert 1111 to Decimal
| Binary digit | 1 | 1 | 1 | 1 |
|---|---|---|---|---|
| Place value | 8 | 4 | 2 | 1 |
| Result | 8 | 4 | 2 | 1 |
Add them up: 8 + 4 + 2 + 1 = 15.
So 1111 in binary equals 15 in decimal. A row of all 1s is always one less than the next power of 2 — here, one less than 16.
Worked Example 3: Convert 1101 to Decimal
Same method, written out in one line: the place values are 8, 4, 2, 1, so 1101 = 8 + 4 + 0 + 1 = 13.
So 1101 in binary equals 13 in decimal.
Worked Example 4: Convert 10101 to Decimal
Five digits this time, so the place values go up to 16: 10101 = 16 + 0 + 4 + 0 + 1 = 21.
So 10101 in binary equals 21 in decimal.
The Powers-of-Two Shortcut
If you convert binary numbers often, memorise the first eight powers of two:
1, 2, 4, 8, 16, 32, 64, 128
With these in your head, converting becomes quick addition. See a 1 under 128, a 1 under 8, and a 1 under 1? The answer is 128 + 8 + 1 = 137 — and the binary number was 10001001. Check it: 128 + 8 + 1 = 137. Correct.
Two facts worth remembering: 10000000 in binary is 128 in decimal, and 11111111 is 255. The number 255 shows up everywhere in computing — it is the biggest value a single byte (8 bits) can hold.
Common Mistakes When Converting Binary to Decimal
1. Reading the binary number as a decimal number. 1010 looks like “one thousand and ten”, but it is not. In binary it is 10. Always remind yourself which system you are reading before you start.
2. Starting the place values from the left. Place values grow from right to left: 1 on the far right, then 2, then 4, and so on. If you start from the left, every answer will be wrong.
3. Forgetting that leading zeros change nothing. 001010 is still 10. The extra zeros on the left add place values of 0. They are just padding.
4. Adding place values where the digit is 0. Only 1s count. In 1010, the 4-place and the 1-place hold 0s, so they add nothing. If you add them anyway, you will overshoot.
Frequently Asked Questions
How do I convert binary to decimal?
Write the powers of two (1, 2, 4, 8, 16…) under the binary digits from right to left, keep the place values where the digit is 1, and add them up. That total is the decimal number.
What is 1010 in decimal?
1010 in binary is 10 in decimal: 8 + 2 = 10.
What is 1111 in decimal?
1111 in binary is 15 in decimal: 8 + 4 + 2 + 1 = 15.
Do I need to learn this, or can I just use a tool?
For one-off conversions, a tool is faster. But if you are studying computer science, networking, or electronics, doing it by hand a few times builds the understanding that makes everything else easier — like how to read binary code in the first place.
Try It Yourself
Pick any binary number and convert it by hand, then check your answer instantly with our free Binary Translator. Try 1010 first — you already know it should come out as 10 — then try a longer one like 1100100 (answer: 100). Once the method clicks, you will find you can do most conversions in your head.