You have a networking or electronics exam and the teacher asks you to turn 110101 into decimal and then hexadecimal. Or you are debugging data and need the real bytes of the word "Añ". Doing it by hand at 11 pm invites mistakes.
How to use Binary to Decimal step by step
1. Choose the mode
Binary → decimal, decimal → binary, text → binary or binary → text.
2. Type or paste the input
In binary you can separate with spaces (1010 1010). In decimal, a positive whole number. In text, anything you like.
3. Read and copy the result
It appears instantly. In binary → decimal you also get the value in hexadecimal and octal.
The Step Count: Traditional Friction vs. KorexTools
Converting binary to decimal by hand
- Write the powers of 2 above each digit.
- Add up the ones holding a 1.
- Repeat for hex and octal by grouping 4 and 3 bits.
- Check the result again.
With the KorexTools Binary to Decimal Converter
- Choose the mode.
- Paste the binary or the text.
- Read decimal, hex and octal together.
How to go from binary to decimal by hand and check it in a second
Binary uses only 0 and 1, and each position is worth double the one to its right: 1, 2, 4, 8, 16... To convert to decimal you add up the positions holding a 1. That is why 1010 is 8 + 2 = 10. It is the method taught in computing and electronics classes, and the one behind every file and message that travels over the internet.
For text, UTF-8 encoding is used: each character is one or more 8-bit bytes. "H" is 01001000, and an "ñ" takes two bytes. The converter uses BigInt, so a 70-digit binary converts exactly instead of being rounded as a regular calculator would.
What each mode does
- •Binary → decimal: accepts spaces and numbers of any length, with hexadecimal and octal.
- •Decimal → binary: large positive whole numbers without losing digits.
- •Text → binary: UTF-8 in 8-bit groups separated by a space.
- •Binary → text: checks complete 8-bit groups and warns if they do not form valid text.
Examples
| Binary | Decimal | Note |
|---|---|---|
| 1010 | 10 | 8 + 2 |
| 10000000 | 128 | 2 to the power of 7 |
| 11111111 | 255 | Maximum with 8 bits |
| 01001000 01101111 | Ho | ASCII text |
Common Mistakes and How to Avoid Them
- ⚠️Forgetting that the leftmost bit has the highest value.
- ⚠️Dropping a leading zero from an 8-bit group and misaligning the whole text.
Frequently Asked Questions
How do you convert 1010 from binary to decimal?
Add the positions holding a 1: 8 + 2 = 10. From right to left they are worth 1, 2, 4, 8, 16, and so on.
What is the largest number with 8 bits?
255 (11111111). With 16 bits it is 65,535 and with 32 bits, 4,294,967,295.
Does it work with very long numbers?
Yes. It uses BigInt, so there is no practical digit limit and no loss of precision.
Does it convert negative or decimal numbers?
No. It works with unsigned integers. Two's complement and floating-point numbers are other representations and are not interpreted here.
What I would do if I were in your shoes
«To verify a conversion we run it backwards: turn the decimal into binary and compare with the original. If they match, the sum is right.» — DataKorex Engineering Team