Number Tools
Convert numeral systems, inspect digit structures, and solve exact base and modular arithmetic in your browser.
Popular tools
Hex Converter Lab
Interpret hexadecimal numbers, bytes, text, colors and signed or unsigned integers in one visual browser-local workspace.
Letters-to-Numbers Converter
Convert letters with A=1, A=0, spreadsheet columns, Unicode code points or custom alphabets, including reliable reverse conversion.
Number Base Converter
Convert an integer or exact fractional value between common numeral systems with validated digits and clear base labels. Calculations stay local and avoid floating-point rounding.
Arbitrary Base Converter
Convert exact numbers between bases 2 and 62. Choose the source and destination bases, validate every digit, and copy or download the normalized result.
Binary Number Converter
Convert binary values to another supported numeral system using exact browser-local arithmetic. Invalid binary digits are identified with a useful error instead of producing a misleading result.
Octal Number Converter
Convert octal numbers to decimal and other supported bases with exact arithmetic. The result includes the normalized source and converted representation for easy verification.
Decimal Number Converter
Convert decimal integers and exact fractions into another numeral system. Repeating output is identified explicitly so the conversion does not silently lose precision.
Hexadecimal Number Converter
Convert hexadecimal values into decimal or another supported base. The tool validates each hexadecimal digit and performs the conversion entirely in your browser.
Base Representation Explorer
View one exact integer simultaneously in binary, octal, decimal, hexadecimal, base 3, and base 36. Compare representations without repeatedly opening separate converters.
Add Numbers in Any Base
Add operands written in different bases, normalize them to exact values, and choose the output base. Fractional operands are preserved without premature rounding.
Base Arithmetic Calculator
Add, subtract, multiply, or divide two exact values that may use different bases. Select a result base and receive both the rational value and its representation.
Convert Fraction Between Bases
Convert terminating or repeating fractional representations between bases with exact rational arithmetic. Repeating cycles are shown in parentheses instead of approximated silently.
Floating-Point & Precision
Compare Numbers in Different Bases
Compare two exact values written in different bases without converting through floating point. The report shows both rational values and their ordering.
IEEE 754 Floating-Point Viewer
Inspect Float16, Float32, or Float64 sign, exponent, fraction, bit pattern, hexadecimal form, stored value, and exact representation error.
Decimal to IEEE 754 Converter
Convert a decimal value into Float16, Float32, or Float64 IEEE-style binary and hexadecimal representation with separated fields.
IEEE 754 to Decimal Converter
Decode a binary or hexadecimal Float16, Float32, or Float64 pattern and report its decimal value and component fields.
Floating-Point Error Explorer
Compare an exact decimal arithmetic result with the actual Float32 or Float64 operation and inspect the result's underlying bits.
Next Representable Float Calculator
Find the previous and next representable Float16, Float32, or Float64 values surrounding a supplied number and calculate the local gap.
Precision Loss Analyzer
Show whether an integer survives conversion to Float32 or Float64 exactly and calculate the resulting integer difference.
Decimal Representation Error Analyzer
Compare a finite decimal with its exact stored floating-point rational and report the magnitude and direction of representation error.
Modular Multiplication Calculator
Multiply large integers modulo a selected value without floating-point precision loss. The final residue is normalized and clearly formatted.
Perfect Square Checker
Determine exactly whether an integer is a perfect square and display its integer square root without floating-point rounding.
Float32 Inspector
Inspect the actual single-precision representation of a decimal, including stored value, exact rational value, and rounding error.
Float64 Inspector
Inspect the actual double-precision representation of a decimal with all 64 bits, exact stored rational, and decimal difference.
Machine Epsilon Explorer
Compare machine epsilon and decimal precision across Float16, Float32, and Float64 formats using their actual field sizes.
ULP Calculator
Calculate the unit in the last place around a floating-point value by finding its adjacent representable numbers.
Floating-Point Range Calculator
Report maximum finite, minimum normal, minimum subnormal, machine epsilon, and approximate decimal precision for each floating format.
Digit Intelligence
Calculate Digit Sum
Add every decimal digit in a whole number using exact integer processing. Signed input is accepted while the sign is excluded from the digit total.
Find Digit Frequency
Count occurrences of each digit from zero through nine. The complete frequency report makes missing and dominant digits easy to inspect.
Digit Structure Analyzer
Analyze length, unique digits, frequencies, zeros, runs, repeating groups, sum, product, digital root, and palindrome status together. This combined view avoids many repetitive checks.
Balanced Ternary Converter
Convert decimal integers to balanced ternary and decode balanced digits using 1, 0, and T for minus one. Exact integer processing keeps large conversions reliable.
Negative Base Converter
Convert integers between decimal and configurable negative bases. Validation prevents unsupported bases and digits while exact arithmetic handles large values safely.
Custom Alphabet Number Converter
Convert an integer between numeral systems defined by your own unique digit alphabets. This supports custom bases beyond the usual binary, decimal, and hexadecimal notation.
Subtract Numbers in Any Base
Subtract numbers written in independently selected bases and return an exact result in your chosen base. Clear validation catches incompatible digits before calculation.
Find Minimum Required Base
Inspect a number representation and find the smallest base capable of containing its largest digit. Unsupported symbols are reported clearly.
Validate Number for a Base
Check whether every digit is valid for a selected base and obtain the exact decimal value when valid. Errors identify the offending digit.
Count Digits in a Number
Count decimal digits while ignoring an optional leading sign. Input validation prevents punctuation and separators from being counted as digits.
Calculate Digit Product
Multiply every digit in a whole decimal number and preserve arbitrarily large integer results. Any zero digit correctly makes the product zero.
Calculate Digital Root
Calculate the additive digital root of a decimal integer. The result is produced directly and consistently for zero and signed values.
Calculate Multiplicative Digital Root
Repeatedly multiply digits until one digit remains. The report includes the multiplicative persistence and every verifiable transformation step.
Sort Digits in a Number
Arrange decimal digits in ascending or descending order while preserving duplicates. The operation runs locally and returns a reusable plain-text result.
Reverse Digits in a Number
Reverse the order of all decimal digits in a whole number. Leading zeros created by reversal remain visible in the textual result.
Rotate Digits in a Number
Rotate decimal digits left or right by any signed number of positions. Positions wrap safely around the digit length.
Find Missing Digits
Identify decimal digits that do not occur in the supplied whole number. The result explicitly reports when no digits are missing.
Find Repeating Digit Patterns
Detect adjacent recurring groups in a decimal digit string and report their positions and repeat counts. Output limits prevent unbounded analysis.
Modular Arithmetic
Modulo Calculator
Calculate a mathematically normalized non-negative remainder, including for negative dividends. The selected modulus is validated before processing.
Modular Exponentiation Calculator
Calculate powers such as 7^222 mod 13 efficiently by repeated squaring. The enormous unreduced power is never constructed in memory.
Modular Inverse Calculator
Find an integer inverse under a modulus using the extended Euclidean algorithm. The report verifies the result or explains why no inverse exists.
Chinese Remainder Theorem Calculator
Combine multiple congruences into one solution class. Compatible non-coprime moduli are supported and inconsistent systems receive a clear explanation.
Modular Arithmetic Explorer
Explore all residues, units, additive inverses, and multiplicative inverses for a modulus. The combined report provides a compact educational view of the modular system.
Modular Addition Calculator
Add two integers within a selected modulus and return the normalized residue. Exact integer arithmetic supports values beyond normal JavaScript precision.
Modular Subtraction Calculator
Subtract integers modulo a selected positive modulus. Negative intermediate values are normalized into the standard residue range.
Solve Linear Congruence
Solve equations of the form ax congruent to b modulo m. The engine handles multiple solution classes and detects unsatisfiable congruences.
Extended Euclidean Algorithm
Calculate the greatest common divisor and Bézout coefficients for two integers. A substitution check verifies the reported coefficients exactly.
Congruence Checker
Check whether two integers belong to the same residue class under a selected modulus. Both normalized residues are shown for verification.
Residue Class Generator
Generate every integer in a bounded range that belongs to a selected residue class. Safe limits prevent impractically large output.
Integer Representations & Bitwise
Signed Integer Converter
Inspect a signed integer as a fixed-width binary word, unsigned interpretation, and hexadecimal value. Clear range checks prevent silent overflow.
Two's Complement Converter
Encode signed decimal integers as two's-complement bit patterns or decode fixed-width patterns back to signed values with overflow validation.
Integer Bit Pattern Viewer
Display bit positions, signed and unsigned interpretations, binary, and hexadecimal forms for a fixed-width integer word.
Bitwise Calculator
Calculate AND, OR, XOR, NOT, NAND, NOR, or XNOR within a selected bit width and compare every operand and result representation.
Bit Shift Calculator
Perform fixed-width left, logical-right, or arithmetic-right shifts while showing the exact before-and-after bit patterns.
Bit Mask Calculator
Build an 8, 16, or 32-bit mask interactively by clicking individual bits, then copy its binary, hexadecimal, and decimal forms.
Bit Difference / Hamming Distance Calculator
Compare two fixed-width integer words and count exactly how many corresponding bit positions differ.
Unsigned Integer Converter
Convert an unsigned 8, 16, 32, or 64-bit integer into its signed interpretation, binary pattern, and hexadecimal representation.
One's Complement Converter
Encode and decode one's-complement signed integers, including its distinct negative-zero representation, across standard word widths.
Sign-Magnitude Converter
Convert signed integers to or from sign-magnitude representation and display the sign bit, magnitude field, and complete word.
Bit Rotate Calculator
Rotate an integer word left or right with width-aware wrapping and inspect the resulting decimal, binary, and hexadecimal values.
Count Set Bits
Count one-bits and zero-bits in a selected fixed-width representation using an efficient population-count calculation.
Number Properties & Rationality
Number Property Analyzer
Analyze a supplied integer for sign, parity, primality, square, cube, perfect power, Armstrong, palindrome, triangular, happy, and automorphic properties.
Rational Number Analyzer
Classify exact integers, fractions, finite decimals, π, e, and integer square roots with mathematically careful rationality explanations.
Decimal Rationality Analyzer
Identify terminating or explicitly repeating decimal expansions, detect a reliable period, and produce the corresponding exact reduced fraction.
Multiply Numbers in Any Base
Multiply exact values written in different numeral systems and format the result in a selected base. Large integer and rational calculations remain browser-local.
Divide Numbers in Any Base
Divide exact numbers written in different bases and reveal rational or repeating output accurately. Division by zero and invalid digits produce useful errors.
Repeating Fraction Base Converter
Parse recurring digits such as 0.1(6) exactly and convert the rational value into another numeral system. Parentheses identify repeating cycles unambiguously.
Integer Classification Tool
Classify an integer by sign, parity, prime or composite status, square, cube, triangular, and happy-number properties in one report.
Perfect Cube Checker
Check positive or negative integers for an exact cube root and verify whether the supplied value is a perfect cube.
Perfect Power Checker
Determine whether an integer can be written exactly as an integer base raised to an exponent greater than one.
Triangular Number Checker
Test an integer against the exact triangular-number discriminant and report its sequence index when a match exists.
Polygonal Number Checker
Check whether a non-negative integer belongs to a configurable polygonal sequence from triangles through 100-sided figures.
Happy Number Checker
Follow the repeated sum-of-squared-digits sequence, report every step, and determine whether the integer reaches one.
Armstrong Number Checker
Test whether a number equals the sum of its digits raised to the number of digits using exact integer powers.
Automorphic Number Checker
Square an integer exactly and check whether the result ends with the original number's complete decimal digits.
Specialized Representations & Number Lab
Roman Numeral Converter
Convert integers to canonical Roman numerals or decode Roman notation back to exact decimal values with clear range validation.
Roman Numeral Validator
Validate Roman numeral symbols and ordering, distinguish canonical notation from malformed forms, and show the corrected canonical representation.
Factoradic Converter
Convert non-negative integer ranks to factoradic notation and decode positional factorial digits with strict digit-limit validation.
Gray Code Converter
Convert decimal or binary integers to reflected Gray code and decode Gray patterns back to binary or exact decimal values.
Zeckendorf Representation Calculator
Represent a non-negative integer as a unique sum of nonconsecutive Fibonacci numbers or decode a valid Zeckendorf bit string.
Continued Fraction Converter
Convert exact fractions or finite decimals into continued-fraction terms and list their progressively accurate rational convergents.
Egyptian Fraction Converter
Decompose a positive proper rational number into a sum of distinct unit fractions using an exact greedy algorithm.
Number Lab
Inspect large integers, bases, digits, bits, Roman and specialist representations, exact fractions, and number words in one browser-local workspace.
Binary-Coded Decimal Converter
Encode every decimal digit as a four-bit BCD group or validate and decode grouped BCD bits into an exact integer.
Combinatorial Number System Converter
Convert an exact rank to combinadic indices or calculate a rank from a combination using arbitrary-precision binomial coefficients.
Fibonacci Coding Converter
Encode positive integers as self-delimiting Fibonacci codes or validate and decode Fibonacci-coded binary data locally.
Golomb Coding Converter
Encode or decode non-negative integers with a configurable Golomb parameter and strict incomplete-code validation.
Unary Number Converter
Convert a non-negative integer to unary code or decode a correctly terminated unary sequence with safe output limits.
Numeral Systems
Negadecimal Converter
Encode decimal integers in base negative ten or decode negadecimal input. The converter uses proper negative-base division without a separate sign bit.
Bijective Numeration Converter
Convert positive integers to and from bijective numeration such as spreadsheet-style column labels. Supply a unique alphabet to define the numeral system.
Base Arithmetic & Representation
Convert Decimal Expansion Between Bases
Turn a decimal expansion into an exact fraction and represent it in another base. Terminating and repeating results are clearly distinguished.
Normalize Number Representation
Remove redundant leading zeros and normalize letter casing or signs for a selected numeral system. The normalized form represents the same exact integer.