Number Base Converter
Translate values between Binary, Octal, Decimal, and Hexadecimal. Includes Hex Color preview and ASCII decoding.
Computer Bases
0-1 only
0-9, A-F
Standard Bases
0-7 only
Data Context
Enter a number to see its Bit count, Color value, and ASCII representation.
Related Calculators
Fluency in Machine Language: Binary, Hex & Beyond
The gap between human thought (Decimal) and machine logic (Binary) is bridged by number systems like Hexadecimal and Octal. Whether you are a student learning digital logic, a programmer debugging memory addresses, or a network engineer calculating subnets, our Number Base Converter provides instant, accurate translations across all major radices.
The Four Pillars of Computing
Decimal (Base 10)
HUMAN STANDARDThe system we use daily. It uses 10 digits (0-9). Each position is a power of 10. (1, 10, 100, 1000).
Binary (Base 2)
MACHINE CODEThe language of processors. Uses only 0 and 1 (Off/On states). Each position is a power of 2 (1, 2, 4, 8, 16...).
Hexadecimal (Base 16)
PROGRAMMER SHORTHANDThe compact standard. Uses 0-9 and A-F. One Hex digit represents 4 bits. Two Hex digits represent 1 Byte.
Octal (Base 8)
LEGACY & PERMISSIONSUses digits 0-7. Each digit represents 3 bits. Still widely used for setting file permissions in Linux/Unix systems.
Why Convert Bases?
Web Design (Colors)
Computers store colors as Red, Green, and Blue numbers (0-255). Designers write them as Hex codes (e.g., #FF5733) because it's shorter than writing "Red: 255, Green: 87, Blue: 51".
Networking (IPs/Macs)
A MAC address is just a 48-bit unique serial number, often written in formatting Hex (e.g., 00:1A:2B:3C:4D:5E). IPv6 addresses are exclusively written in Hexadecimal.
System Administration
Setting file permissions (`chmod 777`) relies on Octal. The first digit is Owner, second is Group, third is World. Reading memory dumps is almost always done in Hex.
Common Values Reference
| Decimal | Hex | Binary | Significance |
|---|---|---|---|
| 15 | F | 1111 | Max value of a nibble (4 bits) |
| 255 | FF | 1111 1111 | Max value of a Byte (8 bits) |
| 65,535 | FF FF | 1111... (16 ones) | Max value of 16-bit Int |
| 16,777,215 | FF FF FF | 1111... (24 ones) | TrueColor (White) |
| 1024 | 400 | 100 0000 0000 | 1 Kibibyte (2^10) |
Frequently Asked Questions
Why do we use Hexadecimal (Base 16) in computing?
Binary (0s and 1s) is too long for humans to read comfortably. Hexadecimal is a perfect shorthand because one Hex digit represents exactly 4 bits (a nibble). This means a standard 8-bit Byte can be written as just two Hex digits (e.g., 11111111 in binary becomes FF in Hex). It reduces errors and saves screen space for debugging memory addresses.
How do I convert Binary to Decimal manually?
Read the binary string from right to left, where each position corresponds to a power of 2 (starting at 2^0). For binary 101:
- Rightmost '1' = 1 * 2^0 = 1
- Middle '0' = 0 * 2^1 = 0
- Leftmost '1' = 1 * 2^2 = 4
- Sum: 4 + 0 + 1 = 5.
What is Octal (Base 8) used for today?
Octal was popular in early computing (like the PDP-8) because machines used 12-bit, 24-bit, or 36-bit words, which are divisible by 3 (each Octal digit represents 3 bits). Today, it is mostly seen in Unix/Linux file permissions (e.g., chmod 755), where the digits represent Read(4), Write(2), and Execute(1) permissions for User, Group, and Others.
Why does Base 10 use digits 0-9 but Base 16 uses letters?
Any number system requires a unique single symbol for each digit value. Base 10 needs ten symbols (0-9). Base 16 needs sixteen symbols. Since we ran out of numbers after 9, we started using the alphabet (A=10, B=11, C=12, D=13, E=14, F=15). Just remember that in Hex, '10' actually implies the value 16!
What is the maximum value of a 32-bit integer?
In a 32-bit system, the maximum unsigned integer is 2^32 - 1, which equals 4,294,967,295. In Hexadecimal, this is FFFF FFFF. If you add 1 to this value, it overflows back to 0 (a famous bug in older games like Pac-Man or YouTube view counters).
How are colors represented in Hex?
Web colors use a 6-digit Hex code, representing three distinct Bytes: Red, Green, and Blue (RGB). For #FF5733:
FF(Red) = 255 (Max Intensity)57(Green) = 8733(Blue) = 51 This mixes a strong red with some green and a little blue to make an orange shade.
What is the largest number base?
Theoretically, you can have a base of any size (Base 64 is common for encoding data). However, for standard math, Bases 2, 8, 10, and 16 are the primary ones. Base 60 (Sexagesimal) was used by ancient Babylonians and is why we still have 60 seconds in a minute and 360 degrees in a circle.
Can I convert text to binary with this tool?
This tool is primarily for mathematical value conversion. If you want to convert text string (like 'Hello') into its binary ASCII representation, please use our Text Encoding Converter tool linked below.
What is 0x notation?
The prefix 0x is placed before a number to explicitly tell the computer (and human readers) that the following digits are Hexadecimal. For example, 10 is ten, but 0x10 is sixteen. This notation comes from the C programming language and is now standard in most tech fields.
How many bits are in a Kilobyte?
A Kilobyte (KB) is 1,000 Bytes (decimal) or 1,024 Bytes (binary/KiB). Since 1 Byte = 8 bits, 1 KB is therefore 8,000 bits (decimal) or 8,192 bits (binary). Multiply by 8 whenever going from Bytes to bits!