How to Convert Binary to Decimal

Every computer on Earth counts in binary — strings of 0s and 1s — while humans think in decimal. Converting between the two is one of the first skills every programmer, student, and electronics hobbyist learns, and it's simpler than it looks. This guide teaches you the one method that always works, with fully worked examples.

The positional method (the only method you need)

Binary is a positional number system, exactly like decimal — except each position is worth a power of 2 instead of a power of 10. In decimal, the number 345 means 3×100 + 4×10 + 5×1. In binary, the same idea applies with powers of two:

The recipe: number the positions from right to left starting at 0, multiply each bit (0 or 1) by its position's value, and add everything up. Bits that are 0 contribute nothing, so you only add the values under the 1-bits.

Worked example 1: convert 1010 to decimal

Adding the contributions: 8 + 2 = 10. So 1010₂ = 10₁₀. If you'd rather skip the arithmetic, our binary to decimal converter shows this exact table for any input you type.

Worked example 2: convert 11111111 to decimal

Eight 1-bits means adding every value from the table: 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255. This is worth memorizing: n one-bits always equal 2ⁿ − 1. So 1111₂ = 15, 111111₂ = 63, and 11111111₂ = 255 — the largest value a single byte can hold.

Worked example 3: convert 10101010 to decimal

The 1-bits sit at positions 7, 5, 3, and 1: 128 + 32 + 8 + 2 = 170. Notice the alternating pattern — 10101010₂ (170) and its mirror 01010101₂ (85) come up constantly in networking masks and test data.

Shortcut: the doubling method (left to right)

For long strings, working right-to-left gets tedious. Instead, read left to right: start at 0, and for each bit, double your running total and add the bit. For 1010:

1. Start: 0
2. Bit 1: 0 × 2 + 1 = 1
3. Bit 0: 1 × 2 + 0 = 2
4. Bit 1: 2 × 2 + 1 = 5
5. Bit 0: 5 × 2 + 0 = 10

Same answer, no powers to look up. Try it on 11001: you should get 25.

Worked example 4: a 16-bit number

The method scales to any length. Convert 1101101010110100₂: label positions 15 down to 0 and add the values under the 1-bits — positions 15, 14, 12, 11, 9, 7, 5, 4, 2 — giving 32768 + 16384 + 4096 + 2048 + 512 + 128 + 32 + 16 + 4 = 55988. Tedious by hand, which is exactly why the converter exists, but the process never changes no matter how long the input gets.

Bonus: binary fractions

Positions continue past the binary point with negative powers: 2⁻¹ = 0.5, 2⁻² = 0.25, 2⁻³ = 0.125. So 101.11₂ = 4 + 1 + 0.5 + 0.25 = 5.75. Most converters (including ours) handle integers only, but the positional logic is identical — just keep halving as you move right of the point.

Common mistakes to avoid

• Numbering positions left to right. Positions always start at 0 on the right. The rightmost bit is worth 1, not the leftmost.
• Forgetting that 2⁰ = 1. Anything to the power of 0 is 1 — the rightmost bit contributes its face value.
• Thinking leading zeros change the value. 0001010 is still 10. Zeros on the left are just padding.
• Confusing binary numbers with binary text. Eight bits can also encode a character (01001000 = "H") — that's a different conversion, handled by our binary to text converter.

Binary to decimal quick reference (0–16)

Once you're comfortable going binary → decimal, try the reverse trip with our decimal to binary converter, or group bits in threes to jump straight to octal.

Frequently asked questions

How do I convert binary to decimal?

Label each bit's position from right to left starting at 0, multiply each bit by 2 raised to its position, and add the results. For example, 1010 = (1×8) + (0×4) + (1×2) + (0×1) = 10.

What is 1010 in decimal?

1010 in binary equals 10 in decimal.

What is 11111111 in decimal?

11111111 in binary equals 255 in decimal — eight 1-bits always make 255, since 2⁸ − 1 = 255.

Is there a shortcut for long binary numbers?

Yes: the doubling method. Start at 0, then read bits left to right — for each bit, double your running total and add the bit. For 1010: 0→1→2→5→10.