Use exp(x) for eˣ and mod(a,b) for the remainder. Roots and logarithms may return complex values.
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How to use the base-n calculator
Choose the input base, then enter a valid integer in that base.
Select Convert, or choose a bitwise operation.
For AND, OR or XOR, enter a second integer in the same base. For shifts, enter the shift count in decimal.
Select Calculate to view decimal, binary, octal and hexadecimal results.
Formula and method
Value = Σ digitₖ × baseᵏ; a hexadecimal digit F represents decimal 15
Integer base conversion
A positional numeral system weights digits by powers of its base. Binary uses digits 0–1, octal 0–7 and hexadecimal 0–9 plus A–F. Conversion keeps the integer value and changes its written form. This tool uses BigInt for conversion, so integers above the usual floating-point safe-integer limit can remain exact.
Bitwise operations and shifts
AND keeps bits set in both operands; OR keeps bits set in either; XOR keeps bits set in exactly one. NOT flips all 32 bits of an unsigned word. A left shift can discard high bits, and a right shift introduces zeros. Both results use unsigned 32-bit interpretation.
Solve a quadratic, including complex roots, or a system of two or three simultaneous linear equations. Degenerate quadratic inputs are handled as linear equations.
Evaluate a real-valued function over a range of x values. Choose start, end and step; each table supports up to 201 rows.
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Base-N Calculator worked examples
Convert hexadecimal FF
FF in base 16
Decimal 255; binary 11111111; octal 377
F represents 15, so FF is 15×16+15=255.
Apply a bitwise AND
255 AND 15, decimal
15
The low four bits are set in both operands. Other bits are cleared by AND.
Shift an unsigned word left
4294967295 << 1
4294967294
Shifting the all-ones 32-bit word left discards its top bit and puts zero in the low bit.
READ THE RESULT WITH CONTEXT
Accuracy, notation and limits
Conversions accept signed integers whose magnitude is at most 2¹²⁸−1. Negative converted values use a minus sign rather than a two’s-complement encoding. Fractions and decimal points are not supported.
Bitwise inputs must be unsigned 32-bit integers from 0 through 4,294,967,295. Shift counts are decimal integers from 0 to 31. Left shifts wrap within the 32-bit word; this is different from unbounded integer multiplication by a power of two.