Convert numbers between binary, octal, decimal, hexadecimal and any base up to 62 – with exact BigInt arithmetic, visible calculation steps and fraction support. Everything runs locally in your browser.
General Base Converters
- Number System Converter
Convert any number into binary, octal, decimal, hexadecimal and a custom base of your choice at the same time – with exact BigInt arithmetic, so even very large values never lose precision.
- Any Base Converter
Convert a number between any two bases from 2 to 36 – binary, ternary, octal, decimal, hex, base 32, base 36 and everything in between – exactly, with no size limit.
- Base 2 to 62 Converter
Convert numbers in any base up to 62, where digits are case-sensitive: 0-9, then A-Z for 10-35, then a-z for 36-61.
- Fractional Base Converter
Convert numbers WITH a fractional part between any bases 2-36, using exact fraction arithmetic that detects repeating digits instead of silently rounding them.
Binary and Decimal
- Binary to Decimal Converter
Convert a binary number to decimal by summing the place values – each 1 bit contributes its power of two.
- Decimal to Binary Converter
Convert a decimal number to binary using repeated division by two – the steps panel lists every division and remainder for your exact input, however large.
- Binary Fraction to Decimal Converter
Convert a binary number with a fractional part (such as 101.
- Decimal Fraction to Binary Converter
Convert a decimal fraction to binary by repeated multiplication by two.
Binary and Hex
- Binary to Hex Converter
Convert binary to hexadecimal by splitting the bits into 4-bit groups (nibbles) – each group maps to exactly one hex digit.
- Hex to Binary Converter
Convert hexadecimal to binary by expanding every hex digit into its 4-bit pattern.
Binary and Octal
- Binary to Octal Converter
Convert binary to octal by splitting the bits into 3-bit groups – each group is one octal digit 0-7.
- Octal to Binary Converter
Convert octal to binary by expanding every octal digit into its 3-bit pattern.
Decimal and Hex
- Decimal to Hex Converter
Convert a decimal number to hexadecimal by repeated division by 16 – remainders above 9 become the letters A-F.
- Hex to Decimal Converter
Convert hexadecimal to decimal by summing place values – each digit is multiplied by a power of 16, with A-F standing for 10-15.
- Hex Fraction to Decimal Converter
Convert a hexadecimal number with a fractional part (such as A.
- Decimal Fraction to Hex Converter
Convert a decimal fraction to hexadecimal by repeated multiplication by 16, with exact detection of repeating hex digits – the float notation used in some language literals.
Decimal and Octal
- Decimal to Octal Converter
Convert a decimal number to octal by repeated division by 8, with every division and remainder shown for your input.
- Octal to Decimal Converter
Convert octal to decimal by summing place values – each digit is multiplied by a power of 8.
- Octal Fraction to Decimal Converter
Convert an octal number with a fractional part (such as 7.
- Decimal Fraction to Octal Converter
Convert a decimal fraction to octal by repeated multiplication by 8, with exact repeating-digit detection instead of silent rounding.
Hex and Octal
- Hex to Octal Converter
Convert hexadecimal to octal via binary: each hex digit becomes 4 bits, and the bits regroup into 3-bit octal digits.
- Octal to Hex Converter
Convert octal to hexadecimal via binary: 3-bit octal groups merge into 4-bit hex nibbles.
Signed Number Tools
- Signed Binary to Decimal Converter
Decode a binary bit pattern under all four signed conventions at once – unsigned, sign-magnitude, one’s complement and two’s complement – because the SAME bits mean different numbers under each.
- Decimal to Signed Binary Converter
Encode a signed decimal number – positive or negative – into two’s complement, one’s complement or sign-magnitude at 4 to 64 bits, with the encoding steps shown.
- Two's Complement Calculator
Compute the two’s complement of a value or pattern: invert every bit, then add one.
- One's Complement Calculator
Compute the one’s complement – simply invert every bit.
- Sign-Magnitude Converter
Convert between decimal and sign-magnitude form, where the leftmost bit is purely a sign flag and the rest is the ordinary magnitude – intuitive, but with two zeros.
- Binary Bit Width Converter
Resize a binary value between 4, 8, 16, 32 and 64 bits.
- Fixed-Point Binary Converter
Convert between decimal values and fixed-point Qm.
- IEEE 754 Floating Point Converter
See exactly how a decimal number is stored as an IEEE 754 float or double – sign, exponent and mantissa bits – and why 0.
- Endianness Converter
Swap a value between big-endian and little-endian byte order.
Digital Electronics Tools
- Binary to Gray Code Converter
Convert weighted binary to reflected Gray code with g = b XOR (b >> 1) – in a Gray sequence, consecutive values differ in exactly one bit, which kills glitches in rotary encoders.
- Gray Code to Binary Converter
Convert reflected Gray code back to weighted binary by cascading XOR from the top bit down – each binary bit is the XOR of the previous binary bit with the current Gray bit.
- Decimal to Gray Code Converter
Convert a decimal number straight to Gray code – first to binary, then one XOR pass.
- Gray Code Table Generator
Generate the full decimal-binary-Gray table for 2 to 6 bits.
- BCD to Decimal Converter
Decode binary-coded decimal: each 4-bit group is one decimal digit 0-9.
- Decimal to BCD Converter
Encode a decimal number as BCD – each digit becomes its own 4-bit group, so 429 becomes 0100 0010 1001.
- Excess-3 Code Converter
Convert between decimal and Excess-3 code, where each digit is stored as digit + 3 in four bits – a self-complementing code from the era of decimal arithmetic hardware.
Number System Calculators
- Binary Calculator
Add, subtract, multiply or divide two binary numbers with exact BigInt arithmetic – the addition mode traces every column and carry for your actual operands.
- Binary Addition Calculator
Add two binary numbers with a full column-by-column carry trace – see exactly where 1+1 writes 0 and carries 1, for your actual inputs.
- Binary Subtraction Calculator
Subtract one binary number from another exactly, including negative results – and see why hardware actually subtracts by adding the two’s complement.
- Binary Multiplication Calculator
Multiply two binary numbers exactly, at any length.
- Binary Division Calculator
Divide two binary numbers exactly, returning the integer quotient and the remainder separately – the form long division and hardware dividers actually produce.
- Hex Calculator
Add, subtract, multiply or divide hexadecimal numbers exactly – with a decimal cross-check in the result so you can verify at a glance.
- Hex Addition Calculator
Add two hexadecimal numbers exactly – columns carry at 16, so 8 + 9 writes 1 and carries 1, and the decimal cross-check confirms the result.
- Hex Subtraction Calculator
Subtract hexadecimal numbers exactly, including negative results – with borrows worth 16 rather than 10, which is where hand calculations usually slip.
- Hex Multiplication Calculator
Multiply hexadecimal numbers of any size exactly.
- Hex Division Calculator
Divide hexadecimal numbers exactly, returning quotient and remainder in hex with a decimal cross-check – useful for address arithmetic and alignment calculations.
- Octal Calculator
Add, subtract, multiply or divide octal numbers exactly – carries and borrows happen at 8, and the decimal equivalents are shown so every step can be checked.
- Base-N Calculator
Do exact arithmetic in ANY base from 2 to 36 – pick the base, pick the operation, and get the result in that base with a decimal cross-check.
- Binary Bit Shift Calculator
Shift a value left or right and see the bits move – logical shifts insert zeros, arithmetic right shift copies the sign bit, and every shift is a multiply or divide by two.
- Binary Bitmask Calculator
Apply AND, OR, XOR and AND-NOT between a value and a mask, bit by bit – the four operations behind testing, setting, toggling and clearing flags.
Number systems are lenses on the same integers: binary shows the bits hardware stores, hex compresses them for humans, octal survives in permissions, and decimal is where arithmetic intuition lives. The tools below convert between all of them — exactly, with the working shown.
Every converter runs BigInt arithmetic (no 2⁵³ cliff), generates its calculation steps from your actual input, and processes everything locally in your browser. Start with the multi-base converter for orientation, or jump straight to the pair you need.
