Binary to Decimal Converter
Enter a binary number to see its decimal value and which powers of two add up to it.
10 110155452DWorking
1× 25 = 1 × 32 = 321× 23 = 1 × 8 = 81× 22 = 1 × 4 = 41× 20 = 1 × 1 = 1- Total = 45
The method
Each bit is worth a power of 2, starting at 1 on the right and doubling leftwards. Add up the values of the bits that are 1.
Place value: the idea behind every base
In any base, a digit’s worth depends on its column. Each column is worth the base times the column to its right. Tap a digit to change it and watch the total.
1×32 + 1×8 + 1×4 + 1×1 = 45 in decimal
Decimal is the same system with ten digits: 347 is 3×100 + 4×10 + 7×1. Nothing about base 10 is special apart from our ten fingers.
Binary to decimal table
| Binary | Decimal |
|---|---|
| 1 | 1 |
| 10 | 2 |
| 11 | 3 |
| 100 | 4 |
| 101 | 5 |
| 111 | 7 |
| 1000 | 8 |
| 1010 | 10 |
| 1111 | 15 |
| 10000 | 16 |
| 100000 | 32 |
| 1000000 | 64 |
| 1100100 | 100 |
| 10000000 | 128 |
| 11111111 | 255 |
| 100000000 | 256 |
Questions people ask
How do you convert binary to decimal?
Label the bits from the right with 1, 2, 4, 8, 16, 32… and add the labels of every bit that is 1. 1011 = 8 + 2 + 1 = 11.
What is 11111111 in decimal?
255 as an unsigned byte. Read as a signed 8-bit two’s-complement value it is −1. The signed reading is shown under the result.
How many decimal values can n bits hold?
n bits hold 2ⁿ values: 0 to 2ⁿ − 1 unsigned. 8 bits hold 256 values (0–255), 16 bits 65,536 and 32 bits 4,294,967,296.