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Understanding the fundamentals of binary and decimal number systems
The binary number system is a base-2 numeral system that uses only two digits: 0 and 1. Each digit in a binary number is called a bit. Binary is the fundamental language of computers and digital systems.
The decimal number system is a base-10 numeral system that uses ten digits: 0 through 9. This is the number system we use in everyday life for counting and mathematical operations.
Converting binary to decimal involves multiplying each binary digit by its corresponding power of 2 and summing the results. The rightmost digit represents 2^0, the next 2^1, and so on.
| Binary | Decimal |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 10 | 2 |
| 11 | 3 |
| 100 | 4 |
| 101 | 5 |
| 110 | 6 |
| 111 | 7 |
| 1000 | 8 |
| 1001 | 9 |
| 1010 | 10 |
Step-by-step guide to manually convert binary numbers to decimal
Start with your binary number. For example, let's use 1011.
Assign powers of 2 to each digit, starting from the right with 2^0 and increasing by 1 as you move left.
Multiply each binary digit by its corresponding power of 2.
Add up all the results from the previous step to get the decimal equivalent.
So, binary 1011 equals decimal 11.
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Find answers to common questions about binary to decimal conversion
Our converter can handle binary numbers up to 32 bits, which corresponds to decimal numbers up to 4,294,967,295. This covers the range of most common use cases including 32-bit integers.
This specific tool is designed for binary to decimal conversion only. However, we offer a separate Decimal to Binary Converter that you can use for the reverse conversion.
Our converter includes validation that checks for invalid characters. If you enter anything other than 0 or 1, you'll receive an error message prompting you to correct your input.
Binary is used in computers because digital electronic circuits can easily represent and process two states (on/off, high/low voltage) which correspond to 1 and 0. This makes binary the most efficient and reliable system for digital computation.
Our current converter focuses on whole binary numbers. For binary fractions, you would need to consider the fractional part with negative powers of 2 (2^-1, 2^-2, etc.). We may add this functionality in future updates.
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