Why do computers use binary?

Computers use binary (base 2) because electronic circuits naturally represent two states: on (1) and off (0). Every piece of data a computer processes is ultimately stored and manipulated as combinations of these two states. Binary maps directly to transistor logic, making it the most practical number system for digital hardware.

How do you convert decimal to hexadecimal?

To convert decimal to hexadecimal, divide the decimal number by 16 repeatedly, recording the remainder at each step using 0-9 for remainders 0-9 and A-F for remainders 10-15. The hex number is the remainders read from bottom to top. For example, 255 divided by 16 gives 15 remainder 15, which is FF in hex.

What is octal used for?

Octal (base 8) was widely used in early computing because three binary digits map exactly to one octal digit, making it a compact shorthand for binary. Today octal is primarily used in Unix and Linux file permission codes (for example chmod 755) where each octal digit represents three permission bits (read, write, execute).

Numeral System Converter

This numeral system converter converts any non-negative integer between the four positional number systems used in mathematics and computing: decimal (base 10), binary (base 2), octal (base 8), and hexadecimal (base 16). Every number system uses a different set of symbols and a different positional weight, but they all represent the same underlying quantity. Decimal uses digits 0 through 9 and is the system you use every day. Binary uses only 0 and 1, mapping directly to the on/off states of transistors in digital hardware. Octal uses 0 through 7 and is used in Unix file permission codes and some assembly languages. Hexadecimal uses 0 through 9 and then A through F for values 10 to 15, giving a compact notation for large binary numbers because each hex digit represents exactly four binary bits. The converter uses JavaScript's built-in parseInt to parse your input in the selected base, then calls toString with each target base to produce the output. You choose a base from the dropdown, enter an integer in that base using the correct digits for that system (binary accepts only 0 and 1; hex accepts 0-9 and A-F), and all three other representations appear immediately. The result for hex is displayed in uppercase. This tool suits programming students, network engineers working with IP and MAC addresses, system administrators writing chmod permissions, developers debugging bit flags, and anyone who needs to cross-check a value across number bases. The converter handles integers only; it does not support fractional values in any base.

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From base

Value to convert

hexadecimal (base 16)

Decimal255

Binary11111111

Octal377

How it works

The converter calls parseInt(value, base) to parse your input string as a number in the chosen base, producing a standard JavaScript integer. It then calls that integer's .toString(base) method with each target base (2, 8, 10, 16) to produce the output strings. Hexadecimal output is converted to uppercase. If the input contains characters that are not valid for the selected base, they are ignored and the remainder is parsed. Very large integers may lose precision above 2^53 because JavaScript uses 64-bit floating-point internally.

Worked example

Starting from 255 in decimal: parseInt('255', 10) = 255. Calling (255).toString(16) gives 'ff', shown as FF. Calling (255).toString(2) gives '11111111'. Calling (255).toString(8) gives '377'. These match the default values pre-filled in the converter above.

Related calculators

Binary Hex Octal Decimal Converter: enter from any of the four base fields directly and all others update.
Data Storage Converter: convert between bits, bytes, KB, MB, GB and TB.
IP Subnet Calculator: calculate subnets and host ranges using binary IP addressing.
Percent Error Calculator: check the accuracy of a converted value against an expected result.

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