Binary Hex Decimal Converter

Q: How do you convert binary to decimal?

Multiply each binary digit by 2 raised to its position power (starting from 0 on the right) and sum the results. For example, binary 1011 = 1x2^3 + 0x2^2 + 1x2^1 + 1x2^0 = 8 + 0 + 2 + 1 = 11 in decimal.

Q: How do you convert decimal to hexadecimal?

Repeatedly divide the decimal number by 16 and record each remainder. The remainders, read from bottom to top, form the hexadecimal number. Remainders 10-15 are represented by letters A-F. For example, 255 in decimal = FF in hexadecimal.

Q: What is the octal number system?

The octal system is base 8, using digits 0-7. It was commonly used in early computing because it maps cleanly to groups of three binary digits. For example, binary 111 = octal 7, and binary 101010 = octal 52. Octal is still used in Unix file permissions.

Q: Why do computers use binary?

Computers use binary (base 2) because digital circuits have two stable states: on and off, represented as 1 and 0. This maps directly to electrical voltage levels and makes hardware design reliable and simple. All data in a computer — text, images, video — is ultimately stored as sequences of binary digits (bits).

Q: What is hexadecimal used for?

Hexadecimal (base 16) is a compact way to represent binary data. Each hex digit corresponds to exactly 4 binary digits, so one byte (8 bits) is two hex digits. Hex is used for color codes in web design (#FF5733), memory addresses, MAC addresses, and debugging. It is much more readable than long binary strings.

Enter a number in any base and instantly see it converted to binary, hexadecimal, decimal, and octal.

How to Use the Binary Hex Decimal Converter

Enter a number in the input field and select its base from the dropdown (decimal, binary, octal, or hexadecimal). The converter instantly displays the equivalent value in all four number systems. For hexadecimal input, use digits 0–9 and letters A–F. Results update in real time as you type.

Number base conversions are fundamental to computer science and programming. Whether you are debugging memory addresses, working with colour codes, setting Unix file permissions, or studying how computers store data, this tool lets you switch between representations instantly.

Understanding Number Bases

Decimal (base 10) is the number system we use daily, with digits 0–9. Binary (base 2) uses only 0 and 1 and is the foundation of all digital computing. Octal (base 8) uses digits 0–7 and is used in Unix permissions. Hexadecimal (base 16) uses 0–9 and A–F, providing a compact way to represent binary data.

How Base Conversion Works

To convert from any base to decimal, multiply each digit by the base raised to its position power and sum the results. To convert from decimal to another base, repeatedly divide by the target base and record remainders. For instance, decimal 42 in binary: 42 ÷ 2 = 21 r0, 21 ÷ 2 = 10 r1, 10 ÷ 2 = 5 r0, 5 ÷ 2 = 2 r1, 2 ÷ 2 = 1 r0, 1 ÷ 2 = 0 r1. Reading remainders bottom-up: 101010.

Practical Applications

Web developers use hex colour codes like #FF5733 daily. Network engineers work with binary subnet masks. Programmers read hexadecimal memory dumps when debugging. Linux administrators set file permissions using octal notation (chmod 755). Understanding these bases makes you more effective in any technical role.

Frequently Asked Questions

How do you convert binary to decimal?

Multiply each digit by 2 raised to its position power (starting from 0 on the right) and add the results. Binary 1011 = 8 + 0 + 2 + 1 = 11.

How do you convert decimal to hexadecimal?

Repeatedly divide by 16, recording remainders (using A–F for 10–15). Read remainders from bottom to top.

What is the octal number system?

Octal uses base 8 with digits 0–7. Each octal digit maps to exactly 3 binary digits. It is used in Unix file permissions.

Why do computers use binary?

Digital circuits have two stable states (on/off), which map naturally to binary digits 1 and 0, making hardware design reliable and simple.

What is hexadecimal used for?

Hex compactly represents binary data: each hex digit equals 4 binary digits. It is used for colour codes, memory addresses, and MAC addresses.

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