Decimal to Binary Converter

Converting decimal numbers to binary is a fundamental operation in computer science — used when working with bitmasks, flags, file permissions, network subnets, and low-level programming. This tool converts any decimal integer to binary, octal, and hex simultaneously.

Step-by-step guide

1. Enter the decimal number: Type any positive integer in the Input field (e.g. 42).
2. Select Decimal as the input base: Choose Decimal (base 10) from the From base selector.
3. Read the binary output: The Binary field shows the binary representation — for 42 that is 101010.
4. Check if it is a power of two: The Is power of two field is useful when working with memory allocation, bitmasks, or hash table sizes that must be powers of 2.

Frequently asked questions

How many bits does the decimal number 255 need?

8 bits. 255 in binary is 11111111 — all eight bits set. The tool reports bit length in the output.

How do I convert decimal to binary manually?

Repeatedly divide by 2, noting the remainder each time, until the quotient is 0. Reading the remainders in reverse order gives the binary representation. For 42: 42÷2=21 r0, 21÷2=10 r1, 10÷2=5 r0, 5÷2=2 r1, 2÷2=1 r0, 1÷2=0 r1. Reversed: 101010.

What is the binary for Unix file permission 755?

755 in octal is rwxr-xr-x. In binary: 7=111, 5=101, 5=101 — the full 9-bit mask is 111101101.