Use the binary converter for numbers, not text
Need the same integer in binary, decimal, hexadecimal, or a less common base? This binary converter lets you select both bases explicitly and returns an exact result with independent decimal and hexadecimal checks. Start with the base used by your source, not the base you want to obtain.
The binary converter starts with 101101 in base 2 and returns 2D when the destination is base 16. The decimal check is 45, so you can compare all three representations without opening separate tabs. Changing an input clears the previous answer, preventing an old result from appearing to describe a new number.
After a successful calculation, use Swap bases in the binary converter to move the answer into the input and reverse the direction. Calculate again to check that you recover the original value. Sample buttons load complete examples, including the appropriate bases; Clear removes the operands while restoring the default settings.
All conversion arithmetic runs in your browser.
Choose the input base before reading the digits
The binary converter validates digits against the input base you select. Before calculating, check the allowed alphabet: binary uses 0 and 1, octal uses 0–7, decimal uses 0–9, and hexadecimal extends that alphabet through F. A valid-looking string can still represent the wrong quantity if you choose the wrong base.
The binary converter supports every integer base from 2 through 36, assigning A through Z to digit values ten through thirty-five. Letter case does not change a digit’s value. A digit must be smaller than its base: 2 is invalid in binary, 8 is invalid in octal, and G is invalid in hexadecimal.
A binary converter cannot infer the intended quantity from a familiar-looking digit string alone. For example, 101 in base 2 is five, while 101 in base 10 is one hundred and one. Always select the input base explicitly rather than guessing from the appearance of the number.
Binary converter example: 101101 to 2D
Try the binary converter with 101101 in base 2 and select base 16 as the destination. The answer should be 2D; tracing the value through decimal explains why. Its binary place values contribute 32, 8, 4, and 1, which add up to 45.
For this binary converter example, divide 45 by 16 to obtain quotient 2 and remainder 13, written D. Divide the quotient 2 by 16 once more: the quotient becomes zero and the remainder is 2. Read those remainders in reverse order to get 2D.
Check the binary converter result by grouping 101101 into 0010 and 1101, which represent hexadecimal 2 and D. These methods agree because sixteen is two to the fourth power. Grouping is convenient for binary and hexadecimal, but repeated division also works for unrelated bases such as seven and thirty-one.
Check long integers without floating-point rounding
Large integers deserve a precision check, not a rounded approximation. The binary converter keeps their complete integer value throughout the operation, including low-order bits that could disappear in a floating-point conversion. Use the trace to understand the method and the result field to obtain the complete numeral.
The binary converter retains low-order bits even when the input is too large for ordinary floating-point integer precision. The trace repeatedly divides the nonnegative magnitude by the target base and records each remainder. Read remainders from the last step back to the first to reconstruct the output.
For a negative value, the binary converter converts the magnitude and then restores the mathematical minus sign. The trace displays at most 64 divisions to keep the page responsive; the main answer is still complete. A truncated trace is therefore a display limit, not a rounded numeric result.
Binary converter input: signs, separators, and width
Formatting should improve readability without silently selecting a signed representation. In the binary converter, a leading minus sign means a negative mathematical integer; spaces and underscores group digits within that integer. They do not define separate values or specify a register width.
The binary converter removes leading zeros from a normalized numeral because they do not change its value. The converter does not preserve a register width or interpret a leading one as a negative sign. In particular, 11111111 means positive 255, not minus one; two’s complement requires a separate width-aware interpretation.
Enter digits in the binary converter without programming prefixes such as 0b or 0x. Decimal fractions, decimal points, exponent notation, and fractions written with a slash are outside this integer tool’s scope. Inputs longer than 4,096 characters are rejected before the arithmetic begins.
Match the conversion to your actual task
A useful result begins with the right question: are your bits a number, a character code, or file data? Use the binary converter when you need the numeric quantity written in another base. Character decoding and file recovery require their own interpretation rules, even when their inputs contain the same zeros and ones.
The binary converter changes a numeral’s base without decoding file structure or character meanings. The binary number 1000001 is decimal 65, while a character decoder may interpret that value as the letter A using ASCII. Those are related but different questions.
After using the binary converter to check a numeric value, choose the ASCII, text, or focused base-pair page when you need its specific interpretation or teaching method. Keeping these tasks distinct helps you catch a wrong assumption before copying a technically correct but irrelevant result.