Base Converter

Advanced Base Converter

Convert between binary, octal, decimal, hexadecimal, and more

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)

Treat as a signed number

Two's complement

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

About Number Bases:

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

Learn more about number bases

Conversion Results

FF

Base	Value
Binary (Base 2)	11111111
Octal (Base 8)	377
Decimal (Base 10)	255
Hexadecimal (Base 16)	FF

Binary Representation

11111111

MSB LSB

Input Base

Base 10

Output Base

Base 16

Bit Length

8 bits

Format	Example
Binary Prefix	0b11111111
Octal Prefix	0o377
Hexadecimal Prefix	0xFF
Formatted Binary	1111_1111

Number Base Examples

Common values in different number bases for reference:

Decimal	Binary	Octal	Hexadecimal	Base32	Base64
0	0	0	0	A	A
1	1	1	1	B	B
2	10	2	2	C	C
3	11	3	3	D	D
4	100	4	4	E	E
5	101	5	5	F	F
6	110	6	6	G	G
7	111	7	7	H	H
8	1000	10	8	I	I
9	1001	11	9	J	J
10	1010	12	A	K	K
15	1111	17	F	P	P
16	10000	20	10	QA	Q
31	11111	37	1F	Z	f
32	100000	40	20	BA	g
63	111111	77	3F	PZ	/
64	1000000	100	40	BAA	BA
100	1100100	144	64	D4	ZG
127	1111111	177	7F	FZ	f/
128	10000000	200	80	GAA	gA
255	11111111	377	FF	PZ	/w
256	100000000	400	100	QAA	BA
511	111111111	777	1FF	PZZ	//
512	1000000000	1000	200	BAAA	BAA
1023	1111111111	1777	3FF	PZZZ	//8
1024	10000000000	2000	400	BAAAA	BBA
2047	11111111111	3777	7FF	PZZZZ	//8
2048	100000000000	4000	800	BAAAAA	BCA
4095	111111111111	7777	FFF	PZZZZZ	///
4096	1000000000000	10000	1000	BAAAAAA	BDA

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