Base Converter

Base Converter

Input Value

Number to Convert

From Base Binary (Base 2) Octal (Base 8) Decimal (Base 10) Hexadecimal (Base 16) Base32 Base64 Custom Base

Custom Base (2-36)

To Base Binary (Base 2) Octal (Base 8) Decimal (Base 10) Hexadecimal (Base 16) Base32 Base64 Custom Base

Custom Base (2-36)

Options

Notation Format Standard (0xFF) Formatted (0b1111_1111) Plain (11111111)

Bit Length Auto 8-bit 16-bit 32-bit 64-bit

Treat as signed Two's complement

Conversion Results

0xFF

All Base Representations

Base	Value
Binary (Base 2)	0b11111111
Octal (Base 8)	0o377
Decimal (Base 10)	255
Hexadecimal (Base 16)	0xFF

Input Base

Base 10

Output Base

Base 16

Bit Length

8 bits (auto)

About Number Bases: Number bases represent numbers using different radices. Common bases include binary (2), octal (8), decimal (10), and hexadecimal (16).

Export Results Auto-save enabled

Supports bases 2-36, Base32, and Base64

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A Base Converter is a tool that transforms numbers between different numeral systems (bases). This is essential in computer science, digital electronics, and mathematics where numbers are represented in various formats like binary (base-2), decimal (base-10), hexadecimal (base-16), and octal (base-8).

Common Number Bases

Base	Name	Digits	Usage
2	Binary	0-1	Computer systems, digital circuits
8	Octal	0-7	Unix file permissions, older systems
10	Decimal	0-9	Everyday arithmetic
16	Hexadecimal	0-9, A-F	Programming, memory addressing

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How Base Conversion Works

1. Converting from Base-N to Decimal (Base-10)

Each digit is multiplied by its positional value (base^position) and summed.

Formula:

$$\text{Decimal}=d_n\times b^n+d_{n-1}\times b^{n-1}+\mathrm{.}\mathrm{.}\mathrm{.}+d_0\times b^0$$

Example: Convert binary 1011 to decimal

$$1\times 2^3+0\times 2^2+1\times 2^1+1\times 2^0=8+0+2+1={11}_{10}$$

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2. Converting from Decimal to Base-N

Repeated division by the target base, collecting remainders in reverse order.

Steps:

1. Divide the number by the target base.

2. Record the remainder.

3. Repeat with the quotient until it reaches 0.

4. The converted number is the remainders read in reverse.

Example: Convert 25 to binary (base-2)

$$\begin{gathered} 25÷2=12\text{ R1} \\ 12÷2=6\text{ R0} \\ 6÷2=3\text{ R0} \\ 3÷2=1\text{ R1} \\ 1÷2=0\text{ R1} \end{gathered}$$

→ Binary = 11001 (read remainders upwards)

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3. Direct Conversions Between Non-Decimal Bases

  A. Binary ↔ Hexadecimal: Group binary digits into 4-bit nibbles.

• 10101100 → 1010 1100 → A C → AC (hex)

  B. Binary ↔ Octal: Group binary digits into 3-bit chunks.

• 101101 → 101 101 → 5 5 → 55 (octal)

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Base Conversion Table (0-15)

Decimal	Binary	Octal	Hexadecimal
0	0000	0	0
1	0001	1	1
2	0010	2	2
3	0011	3	3
4	0100	4	4
5	0101	5	5
6	0110	6	6
7	0111	7	7
8	1000	10	8
9	1001	11	9
10	1010	12	A
11	1011	13	B
12	1100	14	C
13	1101	15	D
14	1110	16	E
15	1111	17	F

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Applications

• Programming: Memory addresses in hex (0xFF), bitwise operations.
• Networking: IP addresses in binary (11000000.10101000...).
• Encryption: Large numbers in different bases for cryptography.
• Digital Circuits: Binary logic gates, FPGA programming.

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Online Base Converters

• RapidTables Base Converter
• Calculator.net Base Calculator
• CyberChef (Advanced Conversions)

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Example Conversions

1. Hex 2F to Decimal:

   $$2\times {16}^1+15\times {16}^0=32+15={47}_{10}$$

2. Decimal 42 to Binary:

   $$42÷2=21R0\to 21÷2=10R1\to 10÷2=5R0\to 5÷2=2R1\to 2÷2=1R0\to 1÷2=0R1$$

   → Binary = 101010

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