Binary to Decimal Converter
Convert numbers between binary, decimal, and hexadecimal.
A whole number written in the source base.
Results update as you type.
How it works
A binary to decimal converter translates whole numbers between the three number systems that dominate computing: binary (base 2), decimal (base 10), and hexadecimal (base 16). Computers store everything in binary, programmers often read memory and colours in hexadecimal, and humans think in decimal, so moving fluently between these bases is a constant need in software, electronics, and networking work. The conversion is useful whenever numbers cross between how machines represent data and how people read it. A developer debugging a bitmask reads binary, a designer reads a hex colour, and a student learning computer science practises converting by hand. Hexadecimal is especially handy because each hex digit maps neatly to four binary bits, making it a compact shorthand for long binary strings. Seeing a value in all these forms builds intuition for how data is actually stored. The conversion works on a simple principle: any positional base expresses a number as a sum of digits times powers of that base. The converter reads the input digits in their source base to recover the underlying integer, then rewrites that integer in the target base, using letters A to F for the hex digits ten through fifteen. The value is identical in every base; only its notation changes. Programmers, students, and engineers use a number base converter to move between binary, decimal, and hexadecimal quickly and without arithmetic slips.
result = value interpreted in the source base, re-expressed in the target base
Every positional number system represents a value as a sum of digits multiplied by powers of its base: binary uses powers of two, decimal powers of ten, and hexadecimal powers of sixteen. Converting first reads the input digits in their source base to recover the underlying integer value, then rewrites that same value using the target base's digits. The number itself never changes; only its written representation does, which is why any base can convert losslessly to any other for whole numbers.
Source:Positional numeral systems (mathematics)
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter value to convert, from base and to base.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Converted value updates instantly as you type — no button to press.
Frequently asked questions
How do I convert binary to decimal by hand?
Write the binary digits and assign each a power of two based on its position, starting at 2 to the power 0 on the right and doubling leftward. Add the powers of two wherever a digit is 1. For 1010, the positions holding 1 are the eights place and the twos place, so 8 plus 2 equals 10. This calculator does the same summation instantly and also handles the reverse and hexadecimal.
Why is hexadecimal used so often in computing?
Hexadecimal is a compact way to write binary because each hex digit represents exactly four binary bits. A byte, eight bits, becomes just two hex digits, which is far easier to read and less error-prone than a long string of ones and zeros. This is why memory addresses, colour codes, and machine values are commonly shown in hex. It bridges human readability and the binary the machine actually uses.
What do the letters A to F mean in hex?
Hexadecimal has sixteen digits, but our decimal system only supplies ten symbols, zero through nine. To represent the values ten through fifteen as single digits, hex borrows the letters A, B, C, D, E, and F. So A is ten, B is eleven, up to F which is fifteen. This lets each hex digit cover all sixteen possible four-bit combinations with a single character.
Can this convert numbers with decimal points?
No, this converter handles whole numbers, or integers, only. Fractional values in different bases involve negative powers of the base and behave differently, and many fractions that are exact in one base repeat endlessly in another, which complicates conversion. For integer work such as bitmasks, addresses, colour values, and typical programming tasks, whole-number conversion is what is needed. Enter only digits valid for your chosen source base.
Why does an invalid value show a dash?
Each base only permits certain digits: binary allows only 0 and 1, decimal allows 0 through 9, and hexadecimal allows 0 through 9 plus A to F. If your input contains a character that is not valid for the source base you selected, such as a 2 in a binary number, the conversion cannot proceed and the result shows a dash. Correct the value to valid digits and it converts immediately.