Binary to Decimal Calculator
Enter a binary number (0s and 1s) to convert it to decimal.
How to Convert Binary to Decimal
Method: positional notation
Multiply each bit by 2 raised to its position (right to left, starting at 0), then sum all values.
Example: 1010 = 1×2³ + 0×2² + 1×2¹ + 0×2&sup0; = 8 + 0 + 2 + 0 = 10
Quick reference
| Binary | Decimal | Hex |
|---|---|---|
| 0000 | 0 | 0 |
| 0001 | 1 | 1 |
| 1000 | 8 | 8 |
| 1010 | 10 | A |
| 1111 | 15 | F |
| 10000 | 16 | 10 |
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How to Convert Binary to Decimal
Each binary digit represents a power of 2, starting from 2⁰ (= 1) at the rightmost position. To convert, multiply each bit by its positional value and sum the results. For example, binary 1011: (1×2³) + (0×2²) + (1×2¹) + (1×2⁰) = 8 + 0 + 2 + 1 = 11 in decimal. This is exactly how your CPU interprets every number it processes — every integer in a program is stored in binary and converted to decimal only for display.
Binary to Decimal Reference Table
| Binary | Decimal | Binary | Decimal |
|---|---|---|---|
| 0000 | 0 | 1000 | 8 |
| 0001 | 1 | 1001 | 9 |
| 0010 | 2 | 1010 | 10 |
| 0100 | 4 | 1100 | 12 |
| 0111 | 7 | 1111 | 15 |
Understanding Binary to Decimal Conversion
Binary (base-2) uses only 0 and 1. Each position represents a power of 2, starting from 2⁰ (rightmost) and doubling left. To convert binary to decimal, multiply each digit by its positional power of 2 and sum the results. For 1011: (1×2³) + (0×2²) + (1×2¹) + (1×2⁰) = 8 + 0 + 2 + 1 = 11. This positional notation is the foundation of all computer data storage.
Binary-to-decimal conversion is essential for reading memory addresses, IP addresses in binary form, color codes in computing, and understanding how computers store integers. An 8-bit byte can store values 0–255 (00000000 to 11111111). A 16-bit word handles 0–65535. Knowing the conversion lets you debug low-level systems, network configurations, and understand computer architecture fundamentals.
Binary to Decimal Reference
| Binary | Decimal | Note |
|---|---|---|
| 0000 | 0 | Zero |
| 0001 | 1 | Smallest positive |
| 1000 | 8 | 2³ |
| 1111 | 15 | Max nibble |
| 11111111 | 255 | Max 8-bit byte |
| 10000000 | 128 | Sign bit (signed) |
The Positional Value Method for Binary Conversion
Converting a binary number to its decimal equivalent relies on the positional value of each bit. In binary, the rightmost position represents 2 raised to the power 0 (which equals 1), the next position represents 2 raised to the power 1 (which equals 2), the next represents 4, then 8, 16, 32, 64, and so on, doubling with each step to the left. To convert, write out the positional values above each binary digit. For every bit that is 1, note the corresponding positional value; for bits that are 0, ignore that position. Add together all the positional values where a 1 appears. The sum is the decimal equivalent. For example, the binary number 1011 has 1s in the positions representing 1, 2, and 8, giving a decimal value of 11. This method works for any length binary number and forms the basis for how computers internally represent and store whole numbers. Practiced regularly, the conversion becomes intuitive for small binary numbers that appear frequently in computing contexts such as permissions (chmod 755) and color codes.
Binary to Decimal Conversion Reference Table
| Binary | Positional values | Decimal |
|---|---|---|
| 0001 | 1 | 1 |
| 0010 | 2 | 2 |
| 0101 | 4 + 1 | 5 |
| 1000 | 8 | 8 |
| 1010 | 8 + 2 | 10 |
| 1111 | 8 + 4 + 2 + 1 | 15 |
| 10000 | 16 | 16 |
| 11111111 | 128+64+32+16+8+4+2+1 | 255 |
