Understanding number systems
Whether you're looking to convert decimal to the binary number system, find the hexadecimal equivalent of an octal value, or work with ASCII, this tool is beneficial. The tool uses four types of number systems and ASCII.
Binary (Base 2)
The binary number system is the fundamental language of computers, consisting of only 0s and 1s. Each digit represents a power of 2. It's often used in computers because of its simplicity.
Example: 1011₂ = (1×2³) + (0×2²) + (1×2¹) + (1×2⁰) = 11₁₀
Decimal (Base 10)
The decimal number system serves as the standard numerical system used by humans, consisting of numbers 0 through 9. It is based on powers of 10.
Example: 345₁₀ = (3×10²) + (4×10¹) + (5×10⁰)
Hexadecimal (Base 16)
The hexadecimal number system is widely used in computing, particularly in addressing and color codes. It uses digits 0-9 and letters A-F and works in base 16, meaning it translates to the power of 16.
Example: 2F₁₆ = (2×16¹) + (15×16⁰) = 47₁₀
Octal (Base 8)
The octal number system works as another base system used in computing, particularly in file permissions in UNIX-based systems.
Example: 75₈ = (7×8¹) + (5×8⁰) = 61₁₀
ASCII (Character Encoding)
ASCII (American Standard Code for Information Interchange) assigns numerical values to characters.
Example: 'A' = 65₁₀, 'B' = 66₁₀
How to use the number system converter
To use the number system converter, simply enter the value in the open box and select its form from the dropdown box on the right. Then, in the second dropdown box, select the form you want to convert to.
Once you make your selections, the tool will calculate the results. You'll see your original input, but you'll also see the new conversion in the results box.
What can you do with the number system converter?
With this tool, you can:
- Convert binary to decimal
- Convert decimal to binary
- Convert hex to ASCII
- Convert ASCII to hex
Essentially, you can perform any conversions between binary, decimal, hex, octal, or ASCII with the number system converter.
Why use a number system converter?
The tool above works as an easy decimal to binary converter, binary to decimal converter, ASCII to hex calculator, and more. If you need to convert between decimal, binary, hexadecimal, octal, or ASCII, the number system converter proves quite useful.
It's especially helpful in the following contexts:
- Programming and development. Low-level programming often requires converting between binary, hexadecimal, and ASCII. You may need to convert a binary number or work with the hexadecimal system.
- Debugging. Tools like debuggers and memory viewers show values in hexadecimal or binary, and you may need to decode ASCII strings.
- Education. The tool helps students understand how values look in different systems.
- Data representation. ASCII shows how characters are stored in memory, making it useful for encoding or decoding information.
What is base 2 versus base 10 measuring systems?
We typically measure bytes using a base 2 (binary) system or a base 10 (decimal) system.
In base 2, each unit is a power of 2. For example, a kilobyte is measured as 2^10 bytes, which equals 1,024 bytes. The base 2 system is favored in computing because it aligns with the binary representation of data by computers.
In base 10, then each unit is a power of 10. For example, we measure a kilobyte as 10^3 bytes, or 1,000 bytes.
Because the base 10 system creates clean numbers like 1,000, marketing and telecommunications fields use it extensively to make capacity expressions easier to understand by the general population. However, it can lead to small discrepancies when compared to the binary system, especially with larger unites such as gigabytes and terabytes.