Binary to Decimal Converter

What Is the Binary to Decimal Converter?

Binary (base 2) is how computers internally represent all data, but it's hard for people to read at a glance -- this converter translates a binary string of 0s and 1s back into a familiar decimal number, and shows the equivalent octal and hexadecimal representations at the same time.

How to Use This Converter

Enter a binary number using only the digits 0 and 1. The result shows the equivalent decimal, octal, and hexadecimal values simultaneously.

How the Conversion Works

Each binary digit represents a power of 2 based on its position -- the rightmost digit is 2⁰ (1), the next is 2¹ (2), then 2² (4), and so on. Adding up the powers of 2 where the binary digit is 1 gives the decimal value.

Worked Examples

Common Values Reference

Practical Uses

Reading a binary value from a debugger, register dump, or networking tool and understanding it as a familiar decimal number. Students and self-taught programmers learning how positional number systems work.

Important Notes

A Faster Way to Read Binary by Hand

Instead of writing out every power of two, you can double as you go. Start from the left with 0. For each digit, double the running total and add the digit. Take 101101: 0 × 2 + 1 = 1; 1 × 2 + 0 = 2; 2 × 2 + 1 = 5; 5 × 2 + 1 = 11; 11 × 2 + 0 = 22; 22 × 2 + 1 = 45. The answer is 45, which matches 32 + 8 + 4 + 1. Both methods agree; use whichever you find easier.

More examples: 11001000 is 128 + 64 + 8 = 200 (hex C8). 11110000 is 240 (hex F0). 1000000000 is 2 to the 9th power, or 512.

Memorizing Useful Anchors

• A single 1 followed by n zeros equals 2 to the power n: 1000 is 8, 10000 is 16, 100000 is 32.
• A run of n ones equals 2 to the power n minus 1: 111 is 7, 1111 is 15, 11111111 is 255.
• Adding a zero on the right doubles the value: 101 is 5 and 1010 is 10.
• The last bit tells you whether the number is odd (1) or even (0).

Checking Your Input

The tool accepts only the characters 0 and 1. Anything else, such as a 2, a letter, a space, or a leading 0b prefix, is treated as invalid. If you copy a value from a debugger that prints spaces between groups, like 1100 1000, remove the spaces before pasting. Leading zeros are fine and do not change the value: 00001010 gives the same result as 1010.

Common Mistakes

The most common mistake is counting positions from the left instead of the right. The rightmost digit is the 1s place. Another error is reading a signed value as unsigned. For example, 11111111 is 255 as unsigned, but in an 8-bit two's complement context it represents -1. The converter here always returns the unsigned reading, so use the Two's Complement Calculator if the data is signed.

A third mistake is entering a bit string that represents something other than an integer, such as a floating-point number or a character code with a defined encoding. The tool will still return the integer value of those bits, but that number may not be the meaning the original data intended.

Limits

The tool uses JavaScript numbers, which are exact for whole numbers up to 9,007,199,254,740,991 (53 binary ones). Longer strings can produce rounded results, so use a big-integer tool for 64-bit values and beyond.

Frequently Asked Questions