Numbers Converter – Convert Between Binary, Decimal, Hex and More

Numbers Converter

Convert numbers between different bases including binary, decimal, hexadecimal, octal and more.

Number Base Converter

Enter Number

From Base

To Base

Converting…

Conversion Result

Converted Value

Decimal Equivalent

Conversion Steps

Base Information

Decimal

Base:

Digits:

0-9

Decimal is the standard base-10 number system used in everyday mathematics. It uses ten digits from 0 to 9.

Hexadecimal

Base:

Digits:

0-9, A-F

Hexadecimal is a base-16 number system commonly used in computing and digital systems. It uses digits 0-9 and letters A-F.

About Number Base Conversion

Understanding Number Bases

A number base, or radix, is the number of unique digits used to represent numbers in a positional numeral system. The most common number system is decimal (base-10), which uses ten digits (0-9). However, different bases are used in various fields for specific purposes.

In any base-N system, each digit represents a power of N, with the rightmost digit representing N^0, the next N^1, and so on. For example, in binary (base-2), the number 101 represents 1×2² + 0×2¹ + 1×2⁰ = 5 in decimal.

Common Number Bases

Binary (Base-2): Uses only 0 and 1. Fundamental in computing as it represents the on/off states of electronic switches.
Octal (Base-8): Uses digits 0-7. Historically used in computing as a more compact representation of binary.
Decimal (Base-10): The standard system for everyday use, using digits 0-9.
Hexadecimal (Base-16): Uses digits 0-9 and letters A-F. Widely used in computing for representing memory addresses and color codes.
Base-36: Uses digits 0-9 and letters A-Z. Useful for creating compact alphanumeric identifiers.

Applications of Different Bases

Different number bases serve specific purposes in various fields:

Computing: Binary is fundamental to how computers process information. Hexadecimal provides a more human-readable way to represent binary data.
Mathematics: Different bases help in understanding number theory and mathematical concepts.
Cryptography: Various bases are used in encoding and decoding information.
Digital Electronics: Different bases are used for different digital systems and protocols.
Programming: Programmers often work with hexadecimal, octal, and binary representations of numbers.

How to Use This Converter

Our number base converter allows you to convert numbers between any two bases from 2 to 36. Simply enter the number you want to convert, select the original base, choose the target base, and click the Convert button. The tool will display the converted value, its decimal equivalent, and step-by-step calculations showing how the conversion was performed.

This converter is particularly useful for students learning about number systems, programmers working with different bases, and anyone who needs to convert numbers between different bases for any purpose.

Frequently Asked Questions

What is the difference between binary and decimal?

Binary (base-2) uses only two digits (0 and 1), while decimal (base-10) uses ten digits (0-9). Binary is the fundamental language of computers, while decimal is the standard system for everyday human use. Each binary digit represents a power of 2, whereas each decimal digit represents a power of 10.

Why is hexadecimal used in computing?

Hexadecimal (base-16) is used in computing because it provides a more compact representation of binary data. Each hexadecimal digit represents exactly four binary digits (bits), making it easier for humans to read and write long binary sequences. It’s commonly used for memory addresses, color codes in web design, and representing binary data in a more readable format.

How do I convert binary to decimal?

To convert binary to decimal, multiply each binary digit by 2 raised to the power of its position (starting from 0 on the right), then sum all the results. For example, binary 1011 = (1×2³) + (0×2²) + (1×2¹) + (1×2⁰) = 8 + 0 + 2 + 1 = 11 in decimal.

What is the highest base that can be used?

Theoretically, there’s no upper limit to the base that can be used, but practically, bases higher than 36 are uncommon because they require additional symbols beyond the 26 letters of the English alphabet. Base-36 is commonly used as the highest practical base, using digits 0-9 and letters A-Z.

How do I convert decimal to hexadecimal?

To convert decimal to hexadecimal, repeatedly divide the decimal number by 16 and record the remainders. The hexadecimal equivalent is the remainders read in reverse order. For remainders 10-15, use letters A-F. For example, decimal 255 ÷ 16 = 15 remainder 15 (F), so 255 in hexadecimal is FF.

What is base-1 (unary) system?

The unary or base-1 system uses only one digit (typically 1) to represent numbers. In this system, the number n is represented by n repetitions of the digit. For example, 3 would be represented as 111. While simple, it’s highly inefficient for representing large numbers and is mainly of theoretical interest.

Why do computers use binary instead of decimal?

Computers use binary because it’s the most practical system for electronic implementation. Binary’s two states (0 and 1) can be easily represented by two distinct physical states, such as on/off voltage levels, magnetic polarity, or light intensity. This simplicity makes binary more reliable and easier to implement in hardware than multi-state systems.

What is the significance of base-60 in time measurement?

Base-60 (sexagesimal) is used in time measurement (60 seconds in a minute, 60 minutes in an hour) and angle measurement (360 degrees in a circle). This system originated with ancient Sumerians and Babylonians, who chose 60 because it has many divisors (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60), making calculations with fractions easier.

How do I convert between non-standard bases?

To convert between any two bases, it’s often easiest to first convert to decimal as an intermediate step. Convert the original number to decimal, then convert the decimal result to the target base. Our converter handles this process automatically for any bases between 2 and 36.

What are floating-point numbers in different bases?

Floating-point numbers in different bases represent numbers with fractional parts using a radix point. For example, in binary, 10.11 represents 2 + 0.5 + 0.25 = 2.75 in decimal. The principles are the same as in decimal, but the base determines the value of each position. Our converter currently handles integer conversions only.

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