Number Base Converter

About Number Systems

Converting numbers between different bases? If you program, work with computers, or study math, you'll run into this constantly. We normally think in base-10 (decimal) because we have 10 fingers, but computers think in base-2 (binary). Programming uses base-16 (hexadecimal) all the time. Each system represents the same number differently, and converting between them is something you'll need to do regularly.

Decimal is what we use every day—0 through 9, then you carry over to the next place. That's base-10 because there are 10 possible digits. It's natural to us, but it's just one way to represent numbers. The number 42 in decimal is the same value as 101010 in binary or 2A in hexadecimal—just different ways of writing it.

Binary uses only 0 and 1. That's base-2—only two possible digits. Computers use binary because they're built on switches that are either on (1) or off (0). Every digit represents a power of 2. The rightmost digit is 2^0 (1), then 2^1 (2), 2^2 (4), and so on. Binary is fundamental to how computers work—all data, instructions, and storage eventually come down to ones and zeros. If you're learning programming or computer science, you'll need to understand binary.

Hexadecimal is base-16. It uses 0 through 9, then A through F to represent 10 through 15. So 10 in decimal is A in hex, 15 is F, and 16 is 10 (which means 1×16 + 0×1). Programmers love hexadecimal because it's a compact way to represent binary. Each hex digit represents exactly 4 binary bits. That 1010 in binary is A in hex, making it way easier to read and work with. You'll see hex everywhere in programming—memory addresses, color codes, character encodings, debugging output.

Octal is base-8, using digits 0 through 7. It's less common now, but you'll still see it. Unix file permissions use octal—that 755 you see means read, write, execute permissions in groups of three bits. Some legacy systems and embedded programming still use octal. It's useful because three binary bits correspond to one octal digit, similar to how four bits equal one hex digit.

Programming is where base conversion comes up most. Memory addresses are often displayed in hexadecimal—seeing 0x7FFF or 0xFF00 is normal. Color codes in web development use hex—#FF0000 is red, #00FF00 is green. When debugging, you might see values in hex or binary and need to convert them to decimal to understand what they actually mean. Bit manipulation, which is common in low-level programming, requires thinking in binary and converting to other bases to verify your work.

Computer science classes constantly involve base conversion. Understanding how numbers work in different bases helps you understand how computers actually process information. Converting between bases helps you see the relationship between them and understand why certain number systems are useful for different purposes.

Networking and system administration use different bases too. IP addresses are sometimes represented in different formats. Subnet masks are easier to understand when you think in binary. File permissions in Unix systems use octal. Converting helps when you're configuring systems or troubleshooting network issues.

Embedded programming and hardware work heavily involve binary and hexadecimal. Microcontrollers, sensors, and low-level hardware communicate in binary or hex. Register values, memory locations, and hardware configuration often require converting between bases. If you're working with Arduino, Raspberry Pi, or similar hardware, you'll be converting bases constantly.

Data analysis sometimes requires base conversion. When you're examining binary data, hexadecimal makes it human-readable. Dump files, packet captures, and binary file analysis often show data in hex that you need to convert to understand. Converting helps you make sense of raw data.

Math and cryptography use different number systems too. Some mathematical concepts are easier to understand in certain bases. Cryptographic algorithms often involve operations in different bases. Converting helps when you're learning these concepts or implementing cryptographic functions.

Web development uses hexadecimal constantly for colors. Every CSS color code is hex. That #FFFFFF is white, #000000 is black. When you're picking colors or working with design, you're using hex whether you realize it or not. Understanding hex helps you work with colors more effectively.

This converter handles all the common bases—binary, decimal, hexadecimal, and octal. You can convert from any base to any other base. No need to do the math manually—just enter your number and pick the bases you want. It's instant and accurate, saving you time when you're programming, debugging, or learning. Whether you're converting a memory address from hex to decimal or checking what a binary number means in regular numbers, this tool makes it easy.

Common Number Systems

Binary (Base-2)

• Uses only 0 and 1
• Fundamental to computer systems
• Each digit represents a power of 2
• Example: 1010 = 10 (decimal)

Decimal (Base-10)

• Uses digits 0-9
• Standard number system for everyday use
• Each digit represents a power of 10
• Example: 42 = 101010 (binary)

Hexadecimal (Base-16)

• Uses digits 0-9 and letters A-F
• Common in programming and memory addresses
• Each digit represents a power of 16
• Example: 2A = 42 (decimal)

Octal (Base-8)

• Uses digits 0-7
• Historical use in computing
• Each digit represents a power of 8
• Example: 52 = 42 (decimal)

Common Uses

Binary

• Computer memory
• Digital logic
• Machine code
• Network protocols

Hexadecimal

• Color codes
• Memory addresses
• Assembly language
• Debugging

Octal

• File permissions (Unix)
• Legacy systems
• Some embedded systems