A clear answer before the details
A base determines the place values used to write a number. Convert to decimal by multiplying each digit by its base power, or convert from decimal using repeated division.
Convert from one base to another
This decimal to binary converter uses an explicit From base and To base, so the same number is never interpreted ambiguously. To convert decimal 10 to binary, enter Number 10, From base 10, and To base 2; the result is 1010. The binary to decimal calculator workflow is the reverse: enter 1010, From base 2, and To base 10 to get 10. Bases from 2 through 36 are accepted.
Hexadecimal, octal, and exact integer conversion
The hexadecimal converter accepts A–Z symbols where appropriate, so FF from base 16 can become 11111111 in base 2. An octal to decimal calculator uses base 8 place values, while a hex to binary conversion groups each hexadecimal digit into four bits. The converter validates every digit against the From base, supports negative integers, and uses exact integer arithmetic for large values instead of floating-point rounding.
Formula guide
The key equations are separated below. Start with the calculator mode, then choose the shape or model that matches your problem.
Positional value
Each digit dᵢ is multiplied by a power of base b.
Binary place values
The powers add to decimal 10.
Worked example
Decimal 10 is binary 1010 because 1×2³ + 0×2² + 1×2¹ + 0×2⁰ = 10.
Formulas for common use cases
Use the matching equation for the problem you are solving, then enter its variables in the calculator above.
Decimal to binary
Use From base 10 and To base 2.
Hexadecimal to binary
Each hexadecimal digit maps to four binary bits.
Octal place values
Every octal digit uses a power of 8.
How to use this calculator
- Enter an integer using the symbols allowed by its source base.
- Choose the source base from 2 to 36.
- Read all converted bases at once.
- Copy individual values for code, notes, or coursework.
Where it helps
Base conversion is useful for programming, debugging, digital logic, networking, and computer-science classes. Binary grouping improves readability, while hexadecimal makes long bit patterns compact. BigInt support keeps large integer conversions exact instead of applying floating-point rounding.
Common mistakes
Every digit must be valid for the selected base. A binary value cannot contain 2, and hexadecimal letters represent values from 10 through 15. This tool is for integers; decimal fractions need a separate positional-conversion method.