Binary to Decimal / Decimal to Binary Converter
Convert binary numbers to decimal and decimal numbers to binary instantly with Tool95’s free online number converter.
What Is a Binary Number?
A binary number is a number written using only two digits: 0 and 1. The binary number system is also called base 2 because it has two possible digits.
Computers and many digital systems use binary because electronic circuits can represent two distinct states. These states can commonly be represented as 0 and 1.
What Is a Decimal Number?
The decimal number system is the base-10 number system used in everyday calculations. It uses ten digits, from 0 through 9.
Each position in a decimal number represents a power of 10. For example, the number 583 can be represented as 5 × 100 + 8 × 10 + 3.
What Is a Binary to Decimal / Decimal to Binary Converter?
A Binary to Decimal / Decimal to Binary Converter is an online utility that converts whole numbers between the binary and decimal number systems.
Tool95’s converter provides both conversion directions in a single tool. Select the required mode, enter the number and click Convert.
How to Use the Binary to Decimal Converter
- Select Binary to Decimal.
- Enter a binary number containing only 0 and 1.
- Click Convert.
- The corresponding decimal value will be displayed instantly.
How to Use the Decimal to Binary Converter
- Select Decimal to Binary.
- Enter a positive or zero whole decimal number.
- Click Convert.
- The corresponding binary representation will be displayed.
How to Convert Binary to Decimal
Binary to decimal conversion uses powers of 2. Starting from the rightmost digit, each position represents an increasing power of 2.
Example: 101101₂
= (1 × 25) + (0 × 24) + (1 × 23) + (1 × 22) + (0 × 21) + (1 × 20)
= 32 + 0 + 8 + 4 + 0 + 1
= 45₁₀
How to Convert Decimal to Binary
One common method for converting a whole decimal number to binary is repeated division by 2. Record the remainder from each division and then read the remainders from bottom to top.
Example: Convert 45 to binary
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 the remainders from bottom to top gives: 101101₂
Binary and Decimal Conversion Examples
| 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 |
Binary Place Values
Each position in a binary number represents a power of 2. The rightmost position is 2⁰, the next is 2¹, followed by 2², 2³ and so on.
2⁵ = 32
2⁴ = 16
2³ = 8
2² = 4
2¹ = 2
2⁰ = 1
Why Computers Use Binary
Digital electronic systems can represent information using two distinct states. Binary provides a simple mathematical way to represent those two states using 0 and 1.
Computer memory, processors, digital communication systems and many other technologies ultimately operate on binary data at a fundamental level.
Binary vs Decimal Number Systems
| Feature | Binary | Decimal |
|---|---|---|
| Base | 2 | 10 |
| Digits | 0 and 1 | 0 through 9 |
| Common Use | Computing and digital systems | Everyday mathematics |
| Place Values | Powers of 2 | Powers of 10 |
Binary Conversion for Students
Binary and decimal conversions are common topics in computer science, information technology and mathematics courses. Practicing manual conversion helps students understand how different number systems represent the same numerical value.
An online converter can be useful for checking the result of a manual calculation after completing the conversion yourself.
Binary Conversion in Computer Science
Binary is fundamental to computer science because digital computers process information using binary states. Understanding binary helps with topics such as computer architecture, digital logic, memory representation and data encoding.
Common Binary Numbers
Small binary values are easy to recognize once the place-value system is understood.
1 = 1
2 = 10
3 = 11
4 = 100
5 = 101
6 = 110
7 = 111
8 = 1000
9 = 1001
10 = 1010
Binary Numbers and Powers of Two
Powers of two are especially important in computing. Some common powers include 2, 4, 8, 16, 32, 64, 128 and 256.
These values appear frequently when discussing memory sizes, binary representation and digital systems.
Binary to Decimal Conversion Tips
- Start with the rightmost binary digit.
- Assign powers of 2 from right to left.
- Multiply each binary digit by its place value.
- Add all the resulting values.
- Check the final result with a calculator if needed.
Decimal to Binary Conversion Tips
- Use repeated division by 2 for whole numbers.
- Record every remainder.
- Continue until the quotient becomes zero.
- Read the remainders in reverse order.
- Verify the result by converting it back to decimal.
Benefits of Using an Online Binary Converter
- Fast number conversion.
- Easy to use.
- Supports both conversion directions.
- Useful for students and developers.
- Reduces manual calculation errors.
- Works in a web browser.
- Mobile-friendly interface.
- Free to use on Tool95.
Important Note About This Converter
This tool is designed primarily for whole-number binary and decimal conversion. Decimal input is interpreted as a whole non-negative integer.
The converter does not interpret decimal fractions such as 10.5 as binary fractions. For specialized floating-point or fractional conversion, a dedicated conversion method is required.
Frequently Asked Questions
What is binary?
Binary is a base-2 number system that uses only the digits 0 and 1.
What is decimal?
Decimal is the base-10 number system commonly used in everyday mathematics and counting.
How do I convert binary to decimal?
Multiply each binary digit by its corresponding power of 2 and add the results together.
How do I convert decimal to binary?
Repeatedly divide the whole decimal number by 2, record the remainders and read them from the last remainder to the first.
What is 1010 in decimal?
Binary 1010 is decimal 10.
What is 1111 in decimal?
Binary 1111 is decimal 15.
Can students use this binary converter?
Yes. Students can use it to check binary and decimal conversions while studying number systems and computer science.
Is the Tool95 Binary Converter free?
Yes. Tool95’s Binary to Decimal / Decimal to Binary Converter is free to use online.