How to convert FF (hex) to 255 (decimal)?

FF in hexadecimal = 255 in decimal

How to convert 42 (decimal) to 2A (hex)?

42 in decimal = 2A in hexadecimal

What is the difference between binary, decimal, and hexadecimal?

Binary is base-2 (uses 0-1), decimal is base-10 (0-9), and hexadecimal is base-16 (0-9, A-F). They are different ways to represent the same number, crucial in computer science. Learn more in our Units Guide.

How do you convert decimal to binary?

To convert a decimal number to binary, you repeatedly divide the decimal number by 2 and record the remainders in reverse order. For example, decimal 10 is binary 1010.

Why is hexadecimal used in programming?

Hexadecimal is a compact way to represent binary data. One hex digit represents four binary digits (a nibble), making it much easier for programmers to read and write binary values, such as memory addresses or color codes.

How do Roman numerals work?

Roman numerals use letters (I, V, X, L, C, D, M) to represent numbers. The value is determined by adding or subtracting these symbols. For example, IV is 4 (5 - 1) and VI is 6 (5 + 1).

Can this tool handle fractions or floating-point numbers?

Currently, this converter is designed for integer conversions between number bases. Support for fractional parts may be added in the future.

Is this number base converter free to use?

Yes, this tool is completely free for all your number system conversion needs. Discover more free tools at UnitConvertNow.

Common Number System Conversions

Decimal to Binary

255 = 11111111

Decimal to Hexadecimal

255 = FF

Decimal to Octal

255 = 377

Binary to Decimal

1010 = 10

Hexadecimal to Decimal

A = 10

Percentage to Decimal

50% = 0.5

Number System Reference

Binary (Base 2)

Digits: 0, 1

Example: 1010 = 10₁₀

Octal (Base 8)

Digits: 0-7

Example: 12 = 10₁₀

Decimal (Base 10)

Digits: 0-9

Example: 10 = 10₁₀

Hexadecimal (Base 16)

Digits: 0-9, A-F

Example: A = 10₁₀

About Number Systems

Number systems are fundamental mathematical frameworks that define how we represent and manipulate numerical values. From the ancient Babylonian base-60 system to modern binary computing, understanding number systems is essential for mathematics, computer science, engineering, and everyday calculations.

What Are Number Systems?

A number system is a mathematical notation for representing numbers using a consistent set of digits or symbols. The base (or radix) of a number system determines how many unique digits are used and how place values are calculated. The most fundamental concept is that each position represents a power of the base.

Key Formula: Positional Notation

In any base-b number system, a number with digits d_nd_n-1...d₁d₀ represents:

d_n × bⁿ + d_n-1 × b^n-1 + ... + d₁ × b¹ + d₀ × b⁰

Common Number Systems and Conversions

System	Base	Digits	Example	Decimal Value
Binary	2	0, 1	1010	10
Octal	8	0-7	12	10
Decimal	10	0-9	10	10
Hexadecimal	16	0-9, A-F	A	10
Roman Numerals	-	I, V, X, L, C, D, M	X	10

Types of Number Systems

Positional Systems

• Binary (Base-2): Foundation of digital computing
• Octal (Base-8): Compact binary representation
• Decimal (Base-10): Standard human counting system
• Hexadecimal (Base-16): Programming and memory addresses
• Duodecimal (Base-12): Time and measurement systems

Non-Positional Systems

• Roman Numerals: Ancient Roman counting system
• Egyptian Hieroglyphs: Ancient Egyptian numerals
• Chinese Numerals: Traditional Chinese counting
• Greek Numerals: Ancient Greek number system
• Unary: Tally marks and counting

Number System Conversion Tools

Converting between number systems requires understanding the mathematical relationships between bases. Modern tools automate these conversions, but understanding the underlying principles is crucial for computer science and engineering applications.

Conversion Methods

Decimal to Other Base: Divide by base, record remainders in reverse order

Other Base to Decimal: Multiply each digit by base^position and sum

Binary ↔ Hexadecimal: Group binary digits in sets of 4, convert each group

Force - Mass - Weight Relationship

While number systems are abstract mathematical concepts, they relate to physical quantities through measurement and calculation. Understanding the relationship between force, mass, and weight demonstrates how numerical representations connect to real-world physics.

Newton's Second Law

The fundamental relationship between force, mass, and acceleration:

F = m × a

Where: F = Force (Newtons), m = Mass (kg), a = Acceleration (m/s²)

Weight Formula

Weight is the force of gravity acting on mass:

W = m × g

Where: W = Weight (Newtons), m = Mass (kg), g = Gravitational acceleration (9.81 m/s²)

Graph: Force vs Mass Relationship

Linear Relationship: F = m × a

When acceleration is constant, force is directly proportional to mass

Mass (kg)

Force (N)

Example: 1 kg mass with 9.81 m/s² acceleration = 9.81 N force

Number System Measurement Tools

Digital Tools

• Scientific Calculators: Built-in base conversion functions
• Programming Languages: Native support for multiple bases
• Online Converters: Instant conversion between systems
• Spreadsheet Software: DEC2BIN, HEX2DEC functions
• Computer Architecture: Hardware-level binary operations

Physical Tools

• Abacus: Ancient counting device
• Slide Rules: Logarithmic calculation tools
• Counting Boards: Medieval calculation devices
• Digital Displays: LED/LCD number representations
• Memory Devices: Binary storage systems

Why Number System Understanding is Important

Computer Science

• Binary arithmetic and logic gates
• Memory addressing and data representation
• Network protocols and data transmission
• Cryptography and security algorithms
• Digital signal processing

Engineering

• Digital circuit design
• Control systems and automation
• Data acquisition and sensors
• Embedded systems programming
• Industrial measurement systems

Mathematics

• Number theory and abstract algebra
• Cryptography and prime factorization
• Mathematical modeling
• Algorithm analysis
• Discrete mathematics

Everyday Applications

• Time and date calculations
• Financial calculations and percentages
• Measurement conversions
• Color codes and hex values
• Digital device interfaces

Real-World Examples

Application	Number System	Example	Real-World Use
Computer Memory	Binary/Hex	0x1A2B3C4D	Memory addresses, data storage
Color Codes	Hexadecimal	#FF5733	Web design, graphics software
File Permissions	Octal	755	Unix/Linux systems
Clock Time	Duodecimal	12:34:56	Time measurement
ISBN Codes	Decimal	978-0-7475-3269-9	Book identification
IP Addresses	Decimal	192.168.1.1	Network addressing

Frequently Asked Questions

Q: Why do computers use binary instead of decimal?

A: Binary uses only two states (0 and 1), which can be easily represented by electronic components like transistors (on/off). This makes digital circuits simpler, more reliable, and less expensive to manufacture than decimal-based systems.

Q: How do I convert between number bases manually?

A: To convert decimal to another base, divide by the base and record remainders in reverse order. To convert from another base to decimal, multiply each digit by the base raised to its position power and sum the results.

Q: What's the relationship between binary and hexadecimal?

A: Hexadecimal is base-16, which is 2⁴. This means each hexadecimal digit represents exactly 4 binary digits (bits). This makes hex a compact way to represent binary data, commonly used in programming and debugging.

Q: Are there number systems with bases higher than 16?

A: Yes, number systems can have any base. Base-32 and base-64 are used in encoding schemes. Base-60 was used by the ancient Babylonians and survives in time and angle measurements. Theoretically, any positive integer can be a base.

Q: How do negative numbers work in different bases?

A: Negative numbers in different bases follow the same principles as decimal. In binary, two's complement is commonly used. The sign is typically indicated by a leading bit or separate sign symbol, depending on the system.

Q: What are the advantages of using different number systems?

A: Each base has advantages: binary for digital electronics, octal for compact binary representation, decimal for human calculations, hexadecimal for programming, and specialized bases for specific applications like time measurement.

Key Takeaways

• Number systems are fundamental to mathematics, computing, and engineering
• Understanding base conversion is essential for computer science
• Different bases serve different practical purposes
• Modern tools make conversion easy, but understanding principles is crucial
• Number systems connect abstract mathematics to real-world applications