How to Use This Converter

Type any number into the input field, then pick its base from the dropdown — decimal, binary, octal, or hex. Hit Convert and all four outputs update at once. You can also click any result directly to use it as the new input and convert from there.

The Four Common Number Bases

Base	Name	Digits Used	Common Use
2	Binary	0, 1	Computer hardware, logic circuits
8	Octal	0-7	Unix file permissions, legacy systems
10	Decimal	0-9	Everyday arithmetic
16	Hexadecimal	0-9, A-F	HTML colors, memory addresses, RGB

How Number Bases Work

Every number system uses positional notation. The position of a digit tells you what power of the base to multiply it by. In decimal (base 10), the number 352 means 3 x 100 + 5 x 10 + 2 x 1. Binary works the same way, but each position is a power of 2 instead of 10. So the binary number 1011 means 1 x 8 + 0 x 4 + 1 x 2 + 1 x 1 = 11 in decimal.

Converting Decimal to Binary

Divide your decimal number by 2 repeatedly. Write down the remainder at each step (always 0 or 1). When you reach 0, read the remainders from bottom to top.

Example: decimal 13 to binary 13 / 2 = 6 remainder 1
6 / 2 = 3 remainder 0
3 / 2 = 1 remainder 1
1 / 2 = 0 remainder 1
Read bottom to top: 1101 - so 13 in binary is 1101.

Hexadecimal in Practice

Hex uses 16 symbols: digits 0-9, then letters A-F. One hex digit equals exactly 4 binary digits, making it a compact shorthand for binary. You see hex in HTML color codes like #FF5733 (three hex pairs for red, green, blue), and in memory addresses throughout programming.

Common Mistakes to Avoid

Octal numbers in code often start with a leading 0 (like 0755 in Unix permissions) - this means something different from decimal 755.
In binary, place values double right-to-left: 1, 2, 4, 8, 16, 32... not 1, 10, 100.
When converting by hand, read binary remainders bottom-to-top, not top-to-bottom.
Hexadecimal letters are case-insensitive - A and a both equal 10 - but be consistent within a project.

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