Convert Binary to Decimal and More
This free binary to decimal converter turns a binary number into decimal — and also converts between decimal, binary, hexadecimal, and octal in one step. Pick the base your number is in, type the value, and the tool shows it in all four number systems at once. It is built for students, programmers, and anyone working close to the metal.
How to Use the Converter
- Select the base your number is currently in (decimal, binary, hex, or octal).
- Type the value.
- Press Convert to see it in decimal, binary, hexadecimal, and octal.
How to Convert Binary to Decimal by Hand
Each binary digit represents a power of two, doubling from right to left: 1, 2, 4, 8, 16, and so on. To convert, add up the place values wherever there is a 1. For example, binary 1011 is 8 + 0 + 2 + 1 = 11 in decimal. Binary 1111 is 8 + 4 + 2 + 1 = 15.
How to Convert Decimal to Binary
Repeatedly divide the decimal number by 2 and record the remainders, then read them bottom to top. 13 ÷ 2 leaves remainders that read as 1101. The calculator handles this automatically and also shows the hexadecimal and octal forms.
Quick Reference Table
| Decimal | Binary | Hex | Octal |
|---|---|---|---|
| 8 | 1000 | 8 | 10 |
| 10 | 1010 | A | 12 |
| 15 | 1111 | F | 17 |
| 255 | 11111111 | FF | 377 |
Why Convert Between Number Bases?
Computers store everything in binary, but people and programs use other bases for convenience: decimal for everyday math, hexadecimal for colors, memory addresses, and byte values, and octal for some file permissions. Being able to convert quickly between them is essential when reading data, debugging, studying computer science, or working with low-level code. This tool removes the manual arithmetic so you can focus on the work.
Frequently Asked Questions
How do I convert binary to decimal?
Add the place values (powers of two) wherever there is a 1. Binary 1011 = 8 + 2 + 1 = 11. The tool does it instantly.
How do I convert decimal to binary?
Divide by 2 repeatedly and read the remainders bottom to top, or just enter the decimal number above and read the binary result.
Does it support hexadecimal and octal?
Yes — it converts between decimal, binary, hexadecimal, and octal in both directions.
Powers of Two
Binary is built on powers of two, and memorizing the first several makes conversions fast: 1, 2, 4, 8, 16, 32, 64, 128, 256. Each position in a binary number is worth one of these values, doubling as you move left. To read a byte like 10110100, add the position values where there is a 1: 128 + 32 + 16 + 4 = 180. The converter does this instantly, but knowing the pattern helps you sanity-check results and understand what is happening.
Where Hexadecimal Shows Up
Hexadecimal is everywhere in computing because each hex digit maps neatly to four binary digits. Color codes (#FF8800), memory addresses, MAC addresses, and byte values are all written in hex to keep long binary strings readable. Converting a hex value such as FF to its decimal equivalent (255) or binary (11111111) is a routine task when reading data dumps, debugging, or studying how computers store information.
A Note on Negative Numbers
This converter works with non-negative whole numbers, which covers the vast majority of everyday conversions and coursework. Representing negative numbers in binary uses a separate scheme called two’s complement, where the leftmost bit signals the sign. If you are studying computer architecture, it is worth learning that method next — but for converting ordinary values between bases, the tool above has you covered.
Binary in Everyday Technology
Binary is not just classroom theory — it underpins everything your devices do. IP addresses, file permissions, color channels, text encoding, and machine instructions all reduce to binary under the hood. When you understand that the byte 11111111 equals 255, it becomes clear why color values and many settings top out at 255, and why memory and storage sizes cluster around powers of two like 256, 512, and 1024. Converting between bases turns these abstract patterns into concrete numbers you can read and work with, which is why the skill stays useful well beyond any single course.