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Binary Converter

Convert Binary to Decimal and more • 4 conversions

Result

0

1 0
Conversion Formula
1 = ---
Quick Reference
1 = 1
10 = 10
50 = 50
100 = 100
500 = 500
1000 = 1000

Unit Explanations

Binaryb

Source Unit

The binary numeral system is a base-2 counting system that uses only two symbols: 0 and 1. Each digit in a binary number represents a power of 2, where the rightmost digit represents 2^0, the next 2^1, and so forth. Binary is fundamental to computer science and digital electronics, as it is the primary language in which computers operate. Information is processed and stored in binary format, making it essential for various algorithms and data structures. In binary representation, each sequence of bits corresponds to a specific numerical or character value.

N = Σ (b^i) where i = position from the right, b = base (2)

Current Use

In contemporary applications, binary is integral to computing and digital systems, serving as the foundation for data representation, storage, and processing. All modern computing devices, including smartphones, personal computers, and servers, rely on binary coding to execute instructions and manage data. Furthermore, programming languages and data formats such as JSON, XML, and HTML utilize binary encoding, enabling seamless communication between devices and applications.

Fun Fact

The largest binary number that can be represented in a single byte is 255 (11111111 in binary).

Decimaldec

Target Unit

The decimal system, also known as the base-10 system, is a method of representing numbers using ten symbols: 0 through 9. It allows for the expression of both whole numbers and fractions, where the position of each digit determines its value based on powers of ten. The decimal point serves as a delimiter between the whole and fractional parts, enabling precise calculations and representations of values. This system is foundational in mathematics and is used universally in finance, science, and everyday counting.

N = d_n * 10^n + d_{n-1} * 10^{n-1} + ... + d_1 * 10^1 + d_0 * 10^0 + d_{-1} * 10^{-1} + ... + d_{-m} * 10^{-m}

Current Use

Today, the decimal system is the predominant numbering system used worldwide across various fields, including mathematics, finance, engineering, and science. It facilitates straightforward calculations and is integral to computer programming, where binary and decimal conversions are essential. Its straightforwardness allows for easy comprehension of mathematical concepts, making it a core element of education in mathematics.

Fun Fact

The concept of zero, essential to the decimal system, was developed in India around the 5th century.

Decimals:
Scientific:OFF

Result

0

1
0
Conversion Formula
1 = ...
1→1
10→10
100→100
1000→1000

All Numbers Conversions

6 converters
Binary
Decimal
Binary
Hex
Decimal
Binary
Decimal
Hex
Hex
Binary
Hex
Decimal

Popular Conversions

Meter → FootKilometer → MileCelsius → FahrenheitKilogram → PoundLiter → GallonSq Meter → Sq FootKm/Hour → Mile/HourPascal → PSI

📐Conversion Formula

= × 1.00000

How to Convert

To convert to , multiply the value by 1.00000. This conversion factor represents the ratio between these two units.

Quick Examples

1
=
1.000
10
=
10.00
100
=
100.0

💡 Pro Tip: For the reverse conversion ( → ), divide by the conversion factor instead of multiplying.

b

Binary

numbers • Non-SI

Definition

The binary numeral system is a base-2 counting system that uses only two symbols: 0 and 1. Each digit in a binary number represents a power of 2, where the rightmost digit represents 2^0, the next 2^1, and so forth. Binary is fundamental to computer science and digital electronics, as it is the primary language in which computers operate. Information is processed and stored in binary format, making it essential for various algorithms and data structures. In binary representation, each sequence of bits corresponds to a specific numerical or character value.

History & Origin

The concept of binary dates back to ancient civilizations, including the Egyptians and Chinese, who recognized the utility of a two-symbol system. However, it was not until the work of Gottfried Wilhelm Leibniz in the 17th century that binary was formally defined as a numeral system. Leibniz's work was pivotal in establishing binary as a foundation for mathematics and logic, linking it to the concept of Boolean algebra.

Etymology: The term 'binary' is derived from the Latin word 'bini', meaning 'two by two' or 'in pairs'. This reflects the foundational aspect of the numeral system based on two symbols.

1679: Gottfried Wilhelm Leibniz publ...1937: George Boole's work on Boolean...1941: The first electronic computer,...

Current Use

In contemporary applications, binary is integral to computing and digital systems, serving as the foundation for data representation, storage, and processing. All modern computing devices, including smartphones, personal computers, and servers, rely on binary coding to execute instructions and manage data. Furthermore, programming languages and data formats such as JSON, XML, and HTML utilize binary encoding, enabling seamless communication between devices and applications.

Information TechnologyTelecommunicationsElectronicsData Science

💡 Fun Facts

  • •The largest binary number that can be represented in a single byte is 255 (11111111 in binary).
  • •The binary system is also used in error detection algorithms, such as checksums and parity bits.
  • •In binary, the number 0 is sometimes referred to as 'false' and 1 as 'true', a concept that underlies Boolean logic.

📏 Real-World Examples

5 b
Binary representation of the decimal number 5
65 b
Storing a character 'A' in ASCII
5 b
Calculating binary addition of 2 and 3
2048 bytes
File size of a small image
1 b
Binary representation of a light switch being ON

🔗 Related Units

Decimal (Decimal is a base-10 numeral system, where each digit represents a power of 10.)Hexadecimal (Hexadecimal is a base-16 numeral system, which can be converted to binary easily.)Octal (Octal is a base-8 numeral system, which can also be represented in binary.)Quinary (Quinary is a base-5 numeral system, representing numbers using five digits.)
dec

Decimal

numbers • Non-SI

Definition

The decimal system, also known as the base-10 system, is a method of representing numbers using ten symbols: 0 through 9. It allows for the expression of both whole numbers and fractions, where the position of each digit determines its value based on powers of ten. The decimal point serves as a delimiter between the whole and fractional parts, enabling precise calculations and representations of values. This system is foundational in mathematics and is used universally in finance, science, and everyday counting.

History & Origin

The decimal system's roots can be traced back to ancient civilizations, including the Egyptians and Babylonians, who utilized base-10 counting methods. However, the modern decimal system was significantly influenced by the work of Indian mathematicians and was later transmitted to Europe through Arabic scholars, who introduced the idea of place value and the concept of zero. This adoption transformed mathematics and commerce, facilitating advanced calculations.

Etymology: The term 'decimal' originates from the Latin word 'decimus', meaning 'tenth'. This highlights its base-10 structure, which is foundational to its function in arithmetic.

500: Indian mathematicians develop ...1202: Fibonacci introduces the decim...1585: Simon Stevin publishes 'De Thi...

Current Use

Today, the decimal system is the predominant numbering system used worldwide across various fields, including mathematics, finance, engineering, and science. It facilitates straightforward calculations and is integral to computer programming, where binary and decimal conversions are essential. Its straightforwardness allows for easy comprehension of mathematical concepts, making it a core element of education in mathematics.

FinanceEducationEngineeringScience

💡 Fun Facts

  • •The concept of zero, essential to the decimal system, was developed in India around the 5th century.
  • •The decimal system is used universally in scientific research, making it easier to share and compare findings across borders.
  • •The longest decimal expansion of pi has over 31 trillion digits, showcasing the complexity of decimal representation.

📏 Real-World Examples

23.99 USD
Calculating the cost of groceries
12.5 cm
Measuring length
2.75 kg
Weight of a package
8.3 L/100km
Fuel consumption
36.6 °C
Temperature reading

🔗 Related Units

Fraction (Fractions can be expressed as decimals (e.g., 1/2 = 0.5).)Binary (Binary is a base-2 system and can be converted to decimal (e.g., 1010 = 10 in decimal).)Percentage (Percentages can be converted to decimals (e.g., 50% = 0.5).)Integer (Integers are whole numbers represented in the decimal system (e.g., 5 is a decimal integer).)

Related Numbers Conversions

Explore more numbers conversions for your calculations.

→Binary to Hex→Decimal to Binary→Decimal to Hex→Hex to Binary→Hex to Decimal

Frequently Asked Questions

How do I convert to ?▼

To convert to , multiply your value by 1. For example, 10 equals 10 .

What is the formula for to conversion?▼

The formula is: = × 1. This conversion factor is based on international standards.

Is this to converter accurate?▼

Yes! MetricConv uses internationally standardized conversion factors from organizations like NIST and ISO. Our calculations support up to 15 decimal places of precision, making it suitable for scientific, engineering, and everyday calculations.

Can I convert back to ?▼

Absolutely! You can use the swap button (⇄) in the converter above to reverse the conversion direction, or visit our to converter.

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