How to Convert Binary to Decimal (With Steps)

To convert binary to decimal, multiply each bit by its power of 2 — starting from the right with 2^0 — and add the results. For example, 1011 in binary equals 11 in decimal: 1 × 8 + 0 × 4 + 1 × 2 + 1 × 1 = 11. That is the whole method; everything below is practice, shortcuts, and the mistakes to avoid.

What Binary and Decimal Actually Mean

Decimal is the base-10 system you use every day: ten digits (0–9), and each position is worth ten times the one to its right. The number 345 means 3 × 100 + 4 × 10 + 5 × 1. Binary is the same idea in base 2: only two digits (0 and 1), and each position is worth twice the one to its right. A binary digit is called a bit.

So where decimal positions are worth 1, 10, 100, 1000, binary positions are worth 1, 2, 4, 8, 16, 32, 64, 128, and so on. The rightmost bit is always worth 1 (2^0), the next one 2 (2^1), then 4 (2^2), then 8 (2^3). Once you see that pattern, every binary number becomes a short addition problem.

The Method, Step by Step

Take the binary number 1011 and work through it slowly:

• Step 1 — Write the bits. 1, 0, 1, 1.
• Step 2 — Label each bit with its power of 2, from the right. From the right, the positions are 2^0, 2^1, 2^2, 2^3 — that is, 1, 2, 4, 8. So the bits line up as: 1 (worth 8), 0 (worth 4), 1 (worth 2), 1 (worth 1).
• Step 3 — Multiply each bit by its position value. 1 × 8 = 8, 0 × 4 = 0, 1 × 2 = 2, 1 × 1 = 1.
• Step 4 — Add the results. 8 + 0 + 2 + 1 = 11.

The zero bits contribute nothing, which is why you can skip them once you are confident — but when you are learning, writing them out prevents the most common error, which is losing track of which position you are on.

A Longer Example

Convert 101101 to decimal. It has six bits, so the position values run from 2^0 up to 2^5:

Add the products: 32 + 0 + 8 + 4 + 0 + 1 = 45. So 101101 in binary is 45 in decimal. Notice how the answer is just the sum of the position values where the bit is 1: 32 + 8 + 4 + 1 = 45. That shortcut — "add the values of the 1 positions" — is the fastest way to convert once the method clicks.

The Doubling Shortcut

There is a second method that many programmers prefer, because it works left to right without powers. Start with the leftmost bit, then for each next bit, double your running total and add the bit:

For 101101: start with 1. Double and add 0 → 2. Double and add 1 → 5. Double and add 1 → 11. Double and add 0 → 22. Double and add 1 → 45. Same answer, and you never need to remember which power you are on. It is worth knowing both methods — the positional method teaches you why conversion works, and the doubling method is faster on paper.

What About Binary Fractions?

The same rule extends past the binary point, using negative powers of 2. In 101.1, the bit after the point is worth 2^-1, which is 0.5. So 101.1 means 4 + 0 + 1 + 0.5 = 5.5. The next fractional bit would be worth 0.25, then 0.125, and so on. Our free Binary to Decimal Converter handles whole binary numbers and shows every step of the working, which is the part students most often need to see.

Common Mistakes to Avoid

The first mistake is labelling positions from the left instead of the right. The leftmost bit of a short number is not worth 1 — the rightmost bit is. Always start from the right. The second mistake is dropping zero bits and shifting everything: 1010 is 10, but 10100 is 20 — one extra zero on the right doubles the value, just as adding a zero to the right of a decimal number multiplies it by ten. The third mistake is mixing up similar-looking numbers: 1011 is 11, 1101 is 13, and 1111 is 15. Writing the position values above the bits catches all three errors before they happen.

Why Computers Use Binary

Computer circuits have two stable states — current flowing or not, on or off — which map directly onto the digits 1 and 0. That is why all data inside a computer, from text to photos to video, is ultimately stored as binary. Converting between binary and decimal is therefore a basic skill for programming students, electronics hobbyists, and anyone studying computer science — and a binary calculator with steps is the fastest way to check your homework and to learn the method at the same time.

Frequently Asked Questions

How do I convert binary to decimal by hand?

Write the binary number, label each bit from the right starting at 2^0, multiply each bit by its position value, and add all the products. For 1011: 1 × 8 + 0 × 4 + 1 × 2 + 1 × 1 = 11.

What is 1011 in decimal?

1011 in binary equals 11 in decimal: the 1 bits sit in the 8, 2 and 1 positions, and 8 + 2 + 1 = 11.

Can I convert binary fractions?

Yes, with negative powers of 2 after the point: the first fractional bit is worth 0.5, the next 0.25, then 0.125. So 101.1 in binary is 5.5 in decimal.

Why do computers use binary?

Computer circuits have two stable states, on and off, which map directly to the digits 1 and 0. Binary is therefore the natural language of computer hardware, and everything inside a machine is stored as bits.