Converting binary to decimal is one of the most useful skills in computing – and it’s simpler than it looks. Every binary digit represents a power of 2, and adding those powers together gives you the decimal value. This guide walks through the method with worked examples you can verify yourself.
The Place-Value Method
Each position in a binary number represents a power of 2, starting from 2⁰ = 1 on the far right and doubling as you move left:
| Position (right → left) | 2⁷ | 2⁶ | 2⁵ | 2⁴ | 2³ | 2² | 2¹ | 2⁰ |
|---|---|---|---|---|---|---|---|---|
| Value | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
To convert, write each binary digit under its place value, multiply, and add up the positions that contain a 1. Positions with 0 contribute nothing.
Worked Example: 1011
Take the binary number 1011:
- Write the place values above each digit: 8, 4, 2, 1
- Multiply: (1 × 8) + (0 × 4) + (1 × 2) + (1 × 1)
- Add: 8 + 0 + 2 + 1 = 11
So 1011₂ = 11₁₀.
Worked Example: 11010
A slightly longer one, 11010:
- Place values: 16, 8, 4, 2, 1
- Multiply: (1 × 16) + (1 × 8) + (0 × 4) + (1 × 2) + (0 × 1)
- Add: 16 + 8 + 0 + 2 + 0 = 26
So 11010₂ = 26₁₀. You can double-check by converting back: 26 = 16 + 8 + 2, which matches the positions of the 1s.
A Shortcut: The Doubling Method
If writing out place values feels slow, use the doubling method – it works left to right:
- Start with 0
- For each binary digit: double your running total, then add the digit
For 101101:
- Start: 0
- Digit 1: 0 × 2 + 1 = 1
- Digit 0: 1 × 2 + 0 = 2
- Digit 1: 2 × 2 + 1 = 5
- Digit 1: 5 × 2 + 1 = 11
- Digit 0: 11 × 2 + 0 = 22
- Digit 1: 22 × 2 + 1 = 45
So 101101₂ = 45₁₀. This method is fast enough to do mentally once you practice.
Converting Binary Fractions
Binary points work like decimal points – positions to the right represent negative powers of 2 (½, ¼, ⅛, …):
| Position | 2² | 2¹ | 2⁰ | . | 2⁻¹ | 2⁻² | 2⁻³ |
|---|---|---|---|---|---|---|---|
| Value | 4 | 2 | 1 | . | 0.5 | 0.25 | 0.125 |
For 101.101:
- Left of the point: (1 × 4) + (0 × 2) + (1 × 1) = 5
- Right of the point: (1 × 0.5) + (0 × 0.25) + (1 × 0.125) = 0.625
- Total: 5.625
Want to skip the manual work? Our binary converter converts binary to decimal instantly and shows the place-value breakdown for every conversion.
Practice Table: Binary 0-31
Use this table to drill conversions until they feel automatic:
| Decimal | Binary | Decimal | Binary |
|---|---|---|---|
| 0 | 0000 | 16 | 10000 |
| 1 | 0001 | 17 | 10001 |
| 2 | 0010 | 18 | 10010 |
| 3 | 0011 | 19 | 10011 |
| 4 | 0100 | 20 | 10100 |
| 5 | 0101 | 21 | 10101 |
| 6 | 0110 | 22 | 10110 |
| 7 | 0111 | 23 | 10111 |
| 8 | 1000 | 24 | 11000 |
| 9 | 1001 | 25 | 11001 |
| 10 | 1010 | 26 | 11010 |
| 11 | 1011 | 27 | 11011 |
| 12 | 1100 | 28 | 11100 |
| 13 | 1101 | 29 | 11101 |
| 14 | 1110 | 30 | 11110 |
| 15 | 1111 | 31 | 11111 |
Notice the pattern: the rightmost column alternates 0, 1, 0, 1…; the next column alternates in pairs (0, 0, 1, 1…); the next in groups of four. Each column to the left cycles at half the speed – that’s the doubling structure of powers of 2 made visible. Cover the binary column and quiz yourself; once you can do 0-31 without hesitation, 8-bit conversions become mechanical.
Common Mistakes to Avoid
- Reading left to right as 1, 2, 4, 8… – the rightmost digit is always 2⁰ = 1. Start from the right.
- Forgetting leading zeros don’t matter – 0011 is still 3, just like 11.
- Mixing up 1010 and 0101 – 1010 = 10, but 0101 = 5. Order matters.
Frequently Asked Questions
How do you convert 11111111 to decimal?
All eight bits are 1, so add every place value: 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255. This is the maximum value of one byte.
What is 10000000 in decimal?
Only the leftmost bit is set, which is 2⁷ = 128.
Is there a quick way to convert binary to decimal in your head?
Yes – memorize the powers of 2 (1, 2, 4, 8, 16, 32, 64, 128) and add the ones where you see a 1. With practice, 8-bit numbers take seconds.
How does binary to decimal relate to hexadecimal?
Every 4 binary digits map to exactly one hex digit (because 2⁴ = 16). So binary → hex → decimal can be a handy two-step path for long strings. Try it in our binary converter, which shows hex and decimal side by side.
