Convert Binary to Decimal
1 Binary (bin) = 1 Decimal (dec). Use the free converter below to instantly convert any binary value to decimal, or view the full conversion table and formula.
1 bin = 1 dec
Binary to Decimal Conversion Table
How to Convert Binary to Decimal
To convert binary to decimal, multiply each digit by 2 raised to the power of its position (rightmost = 0), then sum all values. For example, 1101 in binary: (1×2³) + (1×2²) + (0×2¹) + (1×2⁰) = 8 + 4 + 0 + 1 = 13 in decimal.
Worked Example: Convert 11 bin to dec
Start with the value in binary
11 bin
Apply the formula
Expand each 11 digit × 2^position, sum all values
Calculate the result
11 bin = 3 dec
Binary to Decimal Examples
0 bin is equal to 0 dec. Using the formula Expand each binary digit × 2^position, sum all values, 0 bin converts to 0 dec.
1 bin is equal to 1 dec. Using the formula Expand each binary digit × 2^position, sum all values, 1 bin converts to 1 dec.
10 bin is equal to 2 dec. Using the formula Expand each binary digit × 2^position, sum all values, 10 bin converts to 2 dec.
11 bin is equal to 3 dec. Using the formula Expand each binary digit × 2^position, sum all values, 11 bin converts to 3 dec.
100 bin is equal to 4 dec. Using the formula Expand each binary digit × 2^position, sum all values, 100 bin converts to 4 dec.
101 bin is equal to 5 dec. Using the formula Expand each binary digit × 2^position, sum all values, 101 bin converts to 5 dec.
110 bin is equal to 6 dec. Using the formula Expand each binary digit × 2^position, sum all values, 110 bin converts to 6 dec.
111 bin is equal to 7 dec. Using the formula Expand each binary digit × 2^position, sum all values, 111 bin converts to 7 dec.
Converting Decimal to Binary
Need the reverse conversion? Use the table below for a quick reference converting decimal back to binary.
| Decimal (dec) | Binary (bin) |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 10 |
| 7 | 111 |
| 8 | 1000 |
| 10 | 1010 |
Binary to Decimal FAQ
What is binary?
Binary is a base-2 number system using only digits 0 and 1. It is the fundamental language of computers, where each digit (bit) represents an on/off state.
What is 11111111 in decimal?
11111111 in binary equals 255 in decimal. This represents a full byte with all 8 bits set to 1.
How do I convert binary to decimal?
Multiply each binary digit by 2 raised to the power of its position (starting from 0 on the right), then sum all values. For example, 1010 = (1×8) + (0×4) + (1×2) + (0×1) = 10.
Understanding Binary and Decimal
What is a Binary (bin)?
The binary (bin) is a specialized unit of number systems. It is commonly abbreviated as bin and relates to decimal by a factor of 1.
What is a Decimal (dec)?
The decimal (dec) is a specialized unit of number systems. It is commonly abbreviated as dec and relates to binary by a factor of 1.