How to Convert Binary to Decimal
Each digit in a binary number represents a power of 2. For whole numbers, start with 2^0 = 1 at the rightmost digit and double the place value as you move left.
Step 1: Write down the binary number and line up each digit with its power-of-two place value.
Step 2: Keep the place values where the binary digit is 1 and ignore the places where the digit is 0.
Step 3: Add the remaining place values to get the decimal result.
Example: Binary 1010 = (1×8) + (0×4) + (1×2) + (0×1) = 8 + 0 + 2 + 0 = decimal 10.
Binary Place Values
For an 8-bit binary number, the place values are:
| Binary Position | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
|---|---|---|---|---|---|---|---|---|
| Place Value | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
A 1 means that place value is included in the total. A 0 means it is not.
Step-by-Step Example: 11001010 → 202
Line 11001010 up with the 8-bit place values:
| Place Value | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|---|
| Binary Digit | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 |
Add the active places: 128 + 64 + 8 + 2 = 202. Therefore, binary 11001010 equals decimal 202.
Common Binary to Decimal Conversions
Here are some common binary to decimal conversions:
| Binary | Decimal | Notes |
|---|---|---|
1010 |
10 | Small integer example |
1111 |
15 | Four bits set to 1 |
101010 |
42 | Common tutorial value |
10000000 |
128 | One-byte midpoint |
11000010 |
194 | Extended byte value |
11111111 |
255 | Maximum unsigned byte |
10000000000 |
1024 | Common computing boundary |
Binary Fractions
Binary fractions use powers of 2 to the right of the binary point. The first positions are 1/2, 1/4, 1/8, and so on.
For example, binary 10.101 means 2 + 1/2 + 1/8, which equals decimal 2.625. The interactive converter on this page is focused on ordinary integer conversion, so use this section as a reference for understanding fractional notation.
Signed and Negative Binary Values
A bit pattern does not have one universal negative value by itself. Signed interpretation depends on the chosen bit width and representation, most commonly two’s complement. For example, eight bits of 11111111 can mean unsigned 255 or signed -1 when interpreted as 8-bit two’s complement.
For straightforward base conversion, this page treats binary input as an unsigned value unless the tool explicitly indicates otherwise.
Binary-to-Decimal Input Rules and Common Mistakes
Use this converter for base-2 numbers made from 0 and 1. Spaces can help you read byte groups, but the numeric value comes from the binary digits themselves.
Avoid mixing binary with decimal digits, commas, or unsupported prefixes. For example, 10201 is not valid binary because it contains 2.
- Use
11111111to verify an 8-bit unsigned byte equals 255. - Use
10000000000to verify a binary power of two equals 1024. - Do not assume a signed interpretation unless the bit width and signed format are known.
Related Binary and Base Conversions
Need the reverse operation? Use the decimal to binary converter. To express the same value more compactly, try binary to hexadecimal. The base converter compares values across multiple bases, and the binary, decimal, and hex cheat sheet provides a compact reference table.
When to Use a Binary to Decimal Converter
- Checking byte values while learning computer architecture or networking basics.
- Debugging bit flags, permission masks, and protocol examples in developer documentation.
- Verifying answers for programming exercises, digital logic classes, or interview prep.
- Converting values before moving to hexadecimal or another number system.