Binary / Decimal / Hex Converter

Convert binary, decimal and hexadecimal numbers instantly. Perfect for programming, networking, and computer science.

Decimal

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Conversion Formulas

Binary → Decimal: sum(bit × 2ⁿ)
Decimal → Binary: repeated division by 2
Decimal → Hex: repeated division by 16

What is Binary?

Binary is a base-2 number system using only 0 and 1. It is the fundamental language of computers, CPUs, memory, and digital electronics.

What is Decimal?

Decimal is the base-10 system used in everyday life. It uses digits from 0 to 9 and is the most familiar numbering system to humans.

What is Hexadecimal?

Hexadecimal (Hex) is a base-16 system using digits 0–9 and letters A–F. It is widely used in programming, memory addressing, colors, and debugging.

How to Convert Between Binary, Decimal, and Hex

Choose the source number system.
Apply base conversion rules.
Verify digits match the allowed symbols.

Example: Binary 101010 = Decimal 42 = Hex 2A

Binary, Decimal, and Hexadecimal Conversion Table (0–64)

This table shows how numbers from 0 to 64 are represented in decimal (base-10), binary (base-2), and hexadecimal (base-16). These values are frequently used in programming, networking, memory allocation, and digital electronics.

Decimal	Binary	Hex
0	0	0
1	1	1
2	10	2
3	11	3
4	100	4
5	101	5
6	110	6
7	111	7
8	1000	8
9	1001	9
10	1010	A
11	1011	B
12	1100	C
13	1101	D
14	1110	E
15	1111	F
16	10000	10
20	10100	14
24	11000	18
32	100000	20
40	101000	28
48	110000	30
56	111000	38
64	1000000	40

Why Binary, Decimal, and Hexadecimal Matter

Computers internally operate using binary numbers, while humans naturally work with decimal numbers. Hexadecimal acts as a bridge between the two, offering a compact and readable way to represent long binary sequences.

For example, a single hexadecimal digit represents exactly 4 binary bits, making it ideal for debugging memory, CPU registers, and low-level programming.

Frequently Asked Questions

Why do programmers use hexadecimal?

Because hex is compact and maps cleanly to binary.

Can binary represent all numbers?

Yes, any number can be represented in binary.

Is hex faster than decimal?

No, it is just a representation, not a performance change.

Real-Life Examples

IP addresses are stored in binary internally
HTML color #FF0000 uses hexadecimal
File permissions in Linux use octal/binary logic
CPU instructions are binary encoded
Memory addresses are displayed in hex for readability
Programming: Developers convert decimal user input into binary for CPU processing.
Web Development: CSS colors like #FFFFFF use hexadecimal notation.
Networking: IP addresses are stored in binary even though shown in decimal.
Operating Systems: File permissions rely on binary logic.
Embedded Systems: Sensors and microcontrollers communicate in binary signals.
Game Development: Memory offsets and addresses are displayed in hex.
Cybersecurity: Packet inspection tools show data in hex and binary.

Binary vs Decimal vs Hexadecimal

Each number system serves a specific purpose:

Binary (Base-2): Machine-level representation using 0 and 1.
Decimal (Base-10): Human-friendly numbering system.
Hexadecimal (Base-16): Compact representation of binary data.

Understanding how to convert between these systems is essential for software developers, engineers, students, and IT professionals.