Decimal Converter
A Decimal Converter helps you convert numbers between the decimal number system and other common number systems, including binary, hexadecimal, and octal. The decimal system is the standard number system used in everyday calculations, while other systems are commonly used in computing, programming, and digital electronics.
What Is the Decimal Number System?
The decimal system is a base-10 number system. It uses ten digits: 0 through 9. Each position in a decimal number represents a power of 10.
For example, the number 472 can be expanded as:
4 Γ 102 + 7 Γ 101 + 2 Γ 100
400 + 70 + 2 = 472
Decimal to Binary Conversion
Binary is a base-2 number system that uses only 0 and 1. To convert a whole decimal number to binary, repeatedly divide it by 2 and record each remainder. Read the remainders from bottom to top to obtain the binary result.
For example, converting 25 to binary:
25 Γ· 2 = 12 remainder 1
12 Γ· 2 = 6 remainder 0
6 Γ· 2 = 3 remainder 0
3 Γ· 2 = 1 remainder 1
1 Γ· 2 = 0 remainder 1
Reading the remainders from bottom to top gives:
2510 = 110012
Decimal to Hexadecimal Conversion
Hexadecimal is a base-16 number system. It uses the digits 0β9 and the letters AβF, where A represents 10, B represents 11, and F represents 15.
To convert a decimal number to hexadecimal, repeatedly divide the number by 16 and record the remainders.
For example, 255 divided by 16 gives a quotient of 15 and a remainder of 15. Both 15 values are represented by F in hexadecimal.
Therefore:
25510 = FF16
Decimal to Octal Conversion
Octal is a base-8 number system that uses the digits 0 through 7. Decimal-to-octal conversion follows the same basic division method, but the number is repeatedly divided by 8.
For example, to convert 64 to octal:
64 Γ· 8 = 8 remainder 0
8 Γ· 8 = 1 remainder 0
1 Γ· 8 = 0 remainder 1
Reading the remainders from bottom to top gives:
6410 = 1008
Common Decimal Conversions
| Decimal | Binary | Octal | Hexadecimal |
|---|---|---|---|
| 10 | 1010 | 12 | A |
| 15 | 1111 | 17 | F |
| 16 | 10000 | 20 | 10 |
| 25 | 11001 | 31 | 19 |
| 50 | 110010 | 62 | 32 |
| 100 | 1100100 | 144 | 64 |
| 255 | 11111111 | 377 | FF |
Why Use a Decimal Converter?
Converting numbers manually is useful for learning, but it can become repetitive when working with larger values or several number systems. A Decimal Converter can provide quick results and reduce calculation errors.
These conversions are useful in computer science, programming, digital electronics, networking, mathematics, and information technology. Students can also use them to check their work when learning about different number systems.
Understanding Different Number Bases
The main difference between number systems is their base. Decimal uses base 10, binary uses base 2, octal uses base 8, and hexadecimal uses base 16. The base determines how place values are calculated.
For example, the decimal number 16 is written as 10000 in binary, 20 in octal, and 10 in hexadecimal. Although the representations look different, they all describe the same numerical value.
Things to Check When Converting
Always make sure you are using the correct base and reading the digits according to that system. Binary values cannot contain digits greater than 1, octal values use only 0 through 7, and hexadecimal values can contain A through F.
When converting manually, checking the result by converting it back to decimal is a useful way to confirm that the calculation was performed correctly.
Quick Reference
The decimal system uses 10 digits, binary uses 2, octal uses 8, and hexadecimal uses 16. Knowing these basic relationships makes it easier to understand and convert between common number systems.