Binary ↔ Decimal Converter
Convert binary numbers to decimal and decimal numbers to binary instantly. This free tool runs in your browser, shows the conversion steps, and does not require an account. Enter a number such as 101101 or 45, then copy the result when you need it.
This converter supports unsigned non-negative integers only. It does not convert fractions, negative numbers, or two's-complement signed values.
The result and conversion steps will appear here.
Disclaimer
This Binary ↔ Decimal Converter is provided for general information, study, and educational purposes only. Results are calculated in your browser from the number you enter. The tool converts unsigned non-negative integers between binary (base 2) and decimal (base 10). It does not convert fractions, decimal points, negative numbers, or two's-complement signed values.
Conversion steps are shown to explain the arithmetic. They are not a substitute for coursework requirements, exam answers, or professional engineering review. Web4pps does not provide academic, programming, or electronics advice. Always confirm important calculations independently when they matter for schoolwork, production code, or hardware design.
How to Use Binary ↔ Decimal Converter
Follow these steps to convert a binary number to decimal or a decimal number to binary:
- Choose a conversion direction — Binary → Decimal or Decimal → Binary.
- Enter the number — use only 0 and 1 for binary, or a non-negative whole number for decimal. Spaces are ignored. Leading zeros are allowed.
- Click Convert — or press Enter. The matching result appears in the result panel.
- Read the conversion steps — binary uses powers of 2; decimal uses repeated division by 2.
- Copy, swap, or clear — copy the result, swap the direction (and move the result into the input), or clear the converter. Press Escape to clear.
You can also click Try an example to convert 101101 in binary to 45 in decimal and see the steps.
Who should use Binary ↔ Decimal Converter
This free tool is for anyone who needs a quick, accurate binary conversion without creating an account or sending numbers to a server.
- Students learning binary and number systems.
- Computer science and IT students checking homework or lab work.
- Programmers and developers converting bit patterns and integer values.
- Network and cybersecurity learners working with binary representations.
- Teachers and educators demonstrating positional notation.
- Learners studying digital electronics and computer architecture.
It is not a replacement for a programming language's integer types, a CPU instruction, or signed two's-complement arithmetic. Use it for unsigned whole-number conversion and for seeing how the math works.
What Is Binary?
Binary is the base-2 number system. It uses only two digits, 0 and 1. Each digit is a bit. Computers and digital electronics use binary because circuits can represent two stable states, such as off and on.
Place values in binary are powers of 2: 1, 2, 4, 8, 16, 32, and so on, doubling as you move left. The binary number 1010 means 1×8 + 0×4 + 1×2 + 0×1, which equals 10 in decimal.
What Is Decimal?
Decimal is the base-10 number system used in everyday counting. It uses the digits 0 through 9. Place values are powers of 10: 1, 10, 100, 1,000, and so on.
When people say "the number 45," they almost always mean decimal 45. This converter turns that everyday value into the matching binary bit pattern, or the other way around.
How to Convert Binary to Decimal
Multiply each binary digit by its power of 2, then add the results. The rightmost bit is 2⁰ (ones), the next is 2¹ (twos), then 2² (fours), and so on.
Example: 101101 in binary.
(1 × 2⁵) + (0 × 2⁴) + (1 × 2³) + (1 × 2²) + (0 × 2¹) + (1 × 2⁰)
32 + 0 + 8 + 4 + 0 + 1 = 45
So 101101₂ = 45₁₀. Leading zeros do not change the value: 000101 still equals 5.
How to Convert Decimal to Binary
Repeatedly divide the decimal number by 2 and record the remainder. Continue until the quotient is 0. Then read the remainders from the last calculation to the first.
Example: 45 in decimal.
- 45 ÷ 2 = 22 remainder 1
- 22 ÷ 2 = 11 remainder 0
- 11 ÷ 2 = 5 remainder 1
- 5 ÷ 2 = 2 remainder 1
- 2 ÷ 2 = 1 remainder 0
- 1 ÷ 2 = 0 remainder 1
Reading remainders from bottom to top gives 101101. So 45₁₀ = 101101₂.
Binary to Decimal Examples
Common binary values and their decimal equivalents:
| Binary | Decimal |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 10 | 2 |
| 11 | 3 |
| 100 | 4 |
| 101 | 5 |
| 110 | 6 |
| 111 | 7 |
| 1000 | 8 |
| 1010 | 10 |
| 1111 | 15 |
| 10000 | 16 |
| 101101 | 45 |
Decimal to Binary Examples
Common decimal values and their binary equivalents:
| Decimal | Binary |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 10 |
| 3 | 11 |
| 4 | 100 |
| 5 | 101 |
| 8 | 1000 |
| 10 | 1010 |
| 15 | 1111 |
| 16 | 10000 |
| 25 | 11001 |
| 45 | 101101 |
Binary vs Decimal
Binary and decimal are two ways of writing the same whole numbers. The difference is the base — how many digits the system uses and how place values grow.
| Feature | Binary | Decimal |
|---|---|---|
| Base | 2 | 10 |
| Digits | 0 and 1 | 0 through 9 |
| Place values | Powers of 2 | Powers of 10 |
| Common use | Computers, digital electronics, bit patterns | Everyday counting and arithmetic |
| Example | 101101 | 45 |
Frequently Asked Questions
What is a binary number?
A binary number is a number represented using only the digits 0 and 1. It is the base-2 number system commonly used by computers and digital electronics.
How do I convert binary to decimal?
Multiply each binary digit by its corresponding power of 2 and add the results. The converter does this for you and shows the steps for shorter numbers.
How do I convert decimal to binary?
Repeatedly divide the decimal number by 2 and read the remainders from bottom to top.
What is 1010 in decimal?
1010 in binary equals 10 in decimal.
What is 10 in binary?
10 in decimal equals 1010 in binary.
Can I convert large binary numbers?
Yes. The converter uses BigInt so large integers stay exact. Binary input can be up to 1,024 digits. Values above that limit are rejected instead of being rounded.
Does this converter support negative numbers or fractions?
No. It converts unsigned non-negative whole numbers only. Negative values, decimal points, and fractional bits are rejected with a validation message.
Is this binary converter free?
Yes. You can use it as often as you like at no cost, with no account required.
Are the numbers I enter stored?
Conversions run in your browser. See Privacy Information below for details.
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Privacy Information
The Binary ↔ Decimal Converter runs entirely in your browser. The numbers you enter are used only on your device to compute results. Web4pps does not require an account to use this tool, and conversion inputs are not sent to our servers for storage. Do not enter information you are uncomfortable keeping on your own device while using the page.
