Number converter

Convert numbers between decimal, binary, octal, and hexadecimal number systems with our free Number Converter. Enter a value, select the number system you are converting from and to, and get the result instantly.

The converter is useful for mathematics, programming, computer science, electronics, networking, and other situations where different number bases are used. You can convert values such as decimal to binary, binary to decimal, decimal to hexadecimal, hexadecimal to decimal, and octal conversions in seconds.

Whether you need a quick conversion or want to understand how different number systems work, this page provides both the conversion tool and simple explanations with examples.

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🔢 The Four Main Number Systems

Number systems use different bases to represent numerical values. The base determines which digits can be used and how the position of each digit affects its value.

The four number systems used by this Number Converter are decimal, binary, octal, and hexadecimal.

Decimal – Base 10

The decimal number system is the standard system used in everyday life. It uses ten digits, from 0 to 9.

Each position represents a power of 10. For example:
255 = 2 × 100 + 5 × 10 + 5 × 1

Decimal is commonly used in everyday calculations, mathematics, finance, and general-purpose numerical work.

Binary – Base 2

The binary number system uses only two digits: 0 and 1.

Computers and digital systems use binary because electronic circuits can represent two basic states, such as on and off.

For example:
1011₂ = 11₁₀

Binary numbers are especially common in programming, computer science, networking, and digital electronics.

Octal – Base 8

The octal number system uses eight digits, from 0 to 7.

Octal was historically useful in computing because each octal digit represents three binary digits. It can therefore provide a shorter way to write certain binary values.

For example:
17₈ = 15₁₀

Octal is still encountered in programming, Unix and Linux file permissions, and some technical applications.

Hexadecimal – Base 16

The hexadecimal number system uses sixteen symbols:
0–9 and A–F

The letters represent values from 10 to 15:

• A = 10
• B = 11
• C = 12
• D = 13
• E = 14
• F = 15

For example:
FF₁₆ = 255₁₀

Hexadecimal is widely used in programming, computer memory, machine-level data, color codes, networking, and other areas of computer science.

The Same Value in Different Number Systems

A number can look completely different depending on the number system used, while still representing exactly the same value.

For example:
255 decimal = 11111111 binary = 377 octal = FF hexadecimal

This is why a number base converter is useful: it allows you to switch between different representations of the same numerical value quickly and accurately.

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🔄 How Number Base Conversion Works

Number base conversion means changing a number from one number system to another while keeping the same numerical value. For example, 255 in decimal is the same value as 11111111 in binary and FF in hexadecimal.

The most common number systems use positional notation. This means that the value of a digit depends on both the digit itself and its position within the number.

Place Values and Powers of the Base

In a decimal number, each position represents a power of 10. For example:
255 = 2 × 10² + 5 × 10¹ + 5 × 10⁰

The same principle applies to other bases.

For a binary number, each position represents a power of 2. For example:
1011₂ = 1 × 2³ + 0 × 2² + 1 × 2¹ + 1 × 2⁰

This gives:
8 + 0 + 2 + 1 = 11

So 1011 in binary is 11 in decimal.

Converting Between Number Systems

Different conversion methods can be used depending on the source and target bases.

For example:

• Binary to decimal uses powers of 2.
• Decimal to binary can be calculated using repeated division by 2.
• Decimal to hexadecimal can be calculated using repeated division by 16.
• Hexadecimal to decimal uses powers of 16.
• Binary to hexadecimal can be simplified by grouping binary digits into groups of four.
• Binary to octal can be simplified by grouping binary digits into groups of three.

The important principle is that the representation changes, but the numerical value stays the same.

Our Number Converter performs these calculations automatically, making it easy to convert between decimal, binary, octal, and hexadecimal without calculating each step manually.

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Decimal to Binary and Binary to Decimal

Converting between decimal and binary is one of the most common number base conversions in computing and programming. Decimal uses base 10, while binary uses base 2.

How to Convert Decimal to Binary

To convert a decimal number to binary manually, repeatedly divide the number by 2 and record the remainder from each division.

For example, to convert 25 from decimal to binary:

1. 25 ÷ 2 = 12 remainder 1
2. 12 ÷ 2 = 6 remainder 0
3. 6 ÷ 2 = 3 remainder 0
4. 3 ÷ 2 = 1 remainder 1
5. 1 ÷ 2 = 0 remainder 1

Read the remainders from bottom to top:
25₁₀ = 11001₂

This method works for any positive whole-number decimal value.

How to Convert Binary to Decimal

To convert binary to decimal, multiply each binary digit by its corresponding power of 2 and add the results.

For example:
11001₂

Starting from the right, the place values are:
2⁰, 2¹, 2², 2³, 2⁴

Therefore:
11001₂ = 1 × 2⁴ + 1 × 2³ + 0 × 2² + 0 × 2¹ + 1 × 2⁰

Which gives:
16 + 8 + 0 + 0 + 1 = 25

So:
11001₂ = 25₁₀

Common Decimal to Binary Conversions

Decimal	Binary
1	1
2	10
5	101
10	1010
15	1111
16	10000
25	11001
32	100000
64	1000000
100	1100100
128	10000000
255	11111111

If you need to convert a number quickly, you can use the Number Converter above instead of performing the calculation manually.

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Decimal to Hexadecimal and Hexadecimal to Decimal

Hexadecimal is a base-16 number system that uses the digits 0–9 and the letters A–F. It is widely used in programming, computer science, memory addresses, color codes, and digital systems.

The hexadecimal values are:

Decimal	Hexadecimal
0	0
1	1
2	2
3	3
4	4
5	5
6	6
7	7
8	8
9	9
10	A
11	B
12	C
13	D
14	E
15	F

How to Convert Decimal to Hexadecimal

To convert a decimal number to hexadecimal, repeatedly divide the number by 16 and record the remainder.

For example, convert 255 from decimal to hexadecimal:

1. 255 ÷ 16 = 15 remainder 15
2. 15 ÷ 16 = 0 remainder 15

The decimal value 15 is represented by F in hexadecimal. Reading the remainders from bottom to top gives:
255₁₀ = FF₁₆

Another example is 100 decimal:

1. 100 ÷ 16 = 6 remainder 4
2. 6 ÷ 16 = 0 remainder 6

Therefore:
100₁₀ = 64₁₆

How to Convert Hexadecimal to Decimal

To convert hexadecimal to decimal, multiply each digit by the corresponding power of 16.

For example:
2F₁₆

The place values are 16¹ and 16⁰:
2 × 16¹ + F × 16⁰

Because F = 15:
2 × 16 + 15 × 1 = 32 + 15 = 47

Therefore:
2F₁₆ = 47₁₀

Common Decimal to Hexadecimal Conversions

Decimal	Hexadecimal
10	A
15	F
16	10
25	19
32	20
64	40
100	64
127	7F
128	80
255	FF
256	100
1024	400

You can use the Number Converter above to perform decimal to hexadecimal and hexadecimal to decimal conversions instantly without calculating the powers or divisions manually.

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Decimal to Octal and Octal to Decimal

The octal number system uses base 8 and contains eight digits: 0 through 7. Octal is less common in everyday calculations than decimal, but it is still useful in programming, computer science, and Unix and Linux systems.

How to Convert Decimal to Octal

To convert a decimal number to octal, repeatedly divide the number by 8 and record the remainder from each division.

For example, convert 100 from decimal to octal:

1. 100 ÷ 8 = 12 remainder 4
2. 12 ÷ 8 = 1 remainder 4
3. 1 ÷ 8 = 0 remainder 1

Read the remainders from bottom to top:
100₁₀ = 144₈

Another example is 255 decimal:

1. 255 ÷ 8 = 31 remainder 7
2. 31 ÷ 8 = 3 remainder 7
3. 3 ÷ 8 = 0 remainder 3

Therefore:
255₁₀ = 377₈

How to Convert Octal to Decimal

To convert an octal number to decimal, multiply each digit by its corresponding power of 8.

For example:
144₈

Using the place values of 8:
1 × 8² + 4 × 8¹ + 4 × 8⁰

This gives:
64 + 32 + 4 = 100

Therefore:
144₈ = 100₁₀

Common Decimal to Octal Conversions

Decimal	Octal
1	1
7	7
8	10
10	12
15	17
16	20
25	31
32	40
64	100
100	144
128	200
255	377
256	400
1024	2000

You can use the Number Converter above to quickly convert between decimal and octal without performing the divisions manually.

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Binary, Hexadecimal and Octal Conversions

Binary, hexadecimal, and octal are closely related because they are all commonly used in computing. Converting between them can often be done more efficiently by grouping binary digits instead of first converting through decimal.

Binary to Hexadecimal

Each hexadecimal digit represents exactly four binary digits. This makes binary-to-hexadecimal conversion straightforward.

For example:
11111111₂

Group the binary digits into groups of four:
1111 1111

Each group represents:
1111₂ = F₁₆

Therefore:
11111111₂ = FF₁₆

Another example:
10101100₂

Group the digits:
1010 1100

Which gives:
A C

Therefore:
10101100₂ = AC₁₆

Hexadecimal to Binary

To convert hexadecimal to binary, replace each hexadecimal digit with its four-digit binary equivalent.

For example:
3F₁₆

• 3 = 0011
• F = 1111

Therefore:
3F₁₆ = 00111111₂

Leading zeros can normally be removed when they are not required:
3F₁₆ = 111111₂

Binary to Octal

Each octal digit represents exactly three binary digits.

For example:
110101₂

Group the digits into groups of three:
110 101

Then convert each group:

• 110 = 6
• 101 = 5

Therefore:
110101₂ = 65₈

If the number of binary digits is not divisible by three, add leading zeros before grouping.

Octal to Binary

To convert octal to binary, replace each octal digit with its three-digit binary equivalent.

For example:
57₈

• 5 = 101
• 7 = 111

Therefore:
57₈ = 101111₂

Hexadecimal and Octal

Hexadecimal and octal do not have a simple one-digit-to-one-digit relationship. The easiest method is usually to convert through binary.

For example:
FF₁₆

First convert hexadecimal to binary:
FF₁₆ = 11111111₂

Then group the binary digits into groups of three:
011 111 111

Convert each group to octal:
3 7 7

Therefore:
FF₁₆ = 377₈

This also demonstrates an important relationship between the systems:
255₁₀ = 11111111₂ = 377₈ = FF₁₆

Using these binary groupings makes many conversions between binary, hexadecimal, and octal much faster.

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Number Conversion Examples

The easiest way to understand number base conversion is to work through a few practical examples. The examples below show how the same value can be represented in decimal, binary, octal, and hexadecimal.

Example 1: Convert 10 Decimal to Binary

To convert 10 to binary, divide by 2 and record the remainders:

10 ÷ 2 = 5 remainder 0
5 ÷ 2 = 2 remainder 1
2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1

Reading the remainders from bottom to top:
10₁₀ = 1010₂

Example 2: Convert 25 Decimal to Binary

Using the same method:
25₁₀ = 11001₂

To check the result:
1 × 16 + 1 × 8 + 0 × 4 + 0 × 2 + 1 × 1 = 25

Example 3: Convert 255 Decimal to Hexadecimal

Divide by 16:
255 ÷ 16 = 15 remainder 15

Then:
15 ÷ 16 = 0 remainder 15

Decimal 15 is F in hexadecimal, so:
255₁₀ = FF₁₆

Example 4: Convert 100 Decimal to Octal

Divide by 8:

100 ÷ 8 = 12 remainder 4
12 ÷ 8 = 1 remainder 4
1 ÷ 8 = 0 remainder 1

Reading the remainders from bottom to top:
100₁₀ = 144₈

Example 5: Convert Binary to Decimal

Convert 11010₂ to decimal.

Using powers of 2:
1 × 2⁴ + 1 × 2³ + 0 × 2² + 1 × 2¹ + 0 × 2⁰

This gives:
16 + 8 + 0 + 2 + 0 = 26

Therefore:
11010₂ = 26₁₀

Example 6: Convert Hexadecimal to Binary

Convert A5₁₆ to binary.

Each hexadecimal digit represents four binary digits:

A = 1010
5 = 0101

Therefore:
A5₁₆ = 10100101₂

Example 7: Convert Octal to Binary

Convert 73₈ to binary.

Each octal digit represents three binary digits:

7 = 111
3 = 011

Therefore:
73₈ = 111011₂

One Value in All Four Number Systems

The value 255 provides a useful example because it has common representations in all four systems:

Number System	Representation
Decimal	255
Binary	11111111
Octal	377
Hexadecimal	FF

The numerical value is identical in every case. Only the representation changes.

For quick conversions, enter your value into the Number Converter above and select the number system you are starting with. The converter will calculate the corresponding values in the other number systems automatically.

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Number Conversion Reference Table

The table below shows common values in decimal, binary, octal, and hexadecimal. It can be used as a quick reference when working with different number systems.

Decimal	Binary	Octal	Hexadecimal
0	0	0	0
1	1	1	1
2	10	2	2
3	11	3	3
4	100	4	4
5	101	5	5
6	110	6	6
7	111	7	7
8	1000	10	8
9	1001	11	9
10	1010	12	A
15	1111	17	F
16	10000	20	10
25	11001	31	19
32	100000	40	20
64	1000000	100	40
100	1100100	144	64
127	1111111	177	7F
128	10000000	200	80
255	11111111	377	FF
256	100000000	400	100
512	1000000000	1000	200
1024	10000000000	2000	400

How to Use the Table

Each row represents the same numerical value in four different number systems.

For example:
100 decimal = 1100100 binary = 144 octal = 64 hexadecimal

Similarly:
1024 decimal = 10000000000 binary = 2000 octal = 400 hexadecimal

These examples show why the same number can have very different representations depending on the base being used.

For values that are not included in the table, use the Number Converter above to calculate the conversion instantly.

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Common Number Conversion Mistakes

Number base conversion is straightforward once the basic rules are understood, but a few common mistakes can easily lead to incorrect results.

Using Invalid Digits

Each number system has a specific range of valid digits:

• Binary: 0–1
• Octal: 0–7
• Decimal: 0–9
• Hexadecimal: 0–9 and A–F

For example, 102₂ is not a valid binary number, and 89₈ is not a valid octal number.

Forgetting the Number Base

A value such as 10 can represent different numerical values depending on its base:

• 10₂ = 2 decimal
• 10₈ = 8 decimal
• 10₁₀ = 10 decimal
• 10₁₆ = 16 decimal

Always make sure you know which number system a value belongs to before converting it.

Reading Remainders in the Wrong Order

When converting a decimal number to binary, octal, or hexadecimal using repeated division, the remainders must be read from the last remainder back to the first.

Reading them in the original order produces the wrong result.

Confusing Hexadecimal Letters

In hexadecimal:
A = 10, B = 11, C = 12, D = 13, E = 14, F = 15

The letters are numerical values, not additional characters outside the number system.

Mixing Up Representation and Value

Different representations can look completely different while describing exactly the same value.

For example:
255₁₀ = 11111111₂ = 377₈ = FF₁₆

These are not four different numbers. They are four representations of the same number.

Quick Tip

If you are unsure about a manual calculation, use the Number Converter above to verify your result. This is especially useful when converting larger values or checking hexadecimal and binary calculations.

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Frequently Asked Questions – Number Converter

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