Galois Field GF(2) Calculator

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Want to calculate with decimal operands? You must convert them first. This is an arbitrary-precision binary calculator. It can addsubtractmultiplyor divide two binary numbers. It can operate on very large integers and very small fractional values — binary division online remainder combinations of both. This calculator is, by design, very simple. You can use it to explore binary numbers in their most basic form.

Similarly, you can change the operator and keep the operands as is. Besides the result of the operation, the number of digits in the operands and the result is displayed.

For example, when calculating 1. This means that operand 1 has one digit in its binary division online remainder part and four digits in its fractional part, operand 2 has three digits in its integer part and six digits in its fractional part, and the result has four digits in its integer part and ten digits in its fractional part. Addition, subtraction, and multiplication always produce a finite result, but division may in fact, in most cases produce an infinite repeating fractional value.

Infinite results are truncated — not rounded binary division online remainder to the specified number of bits. For divisions that represent dyadic fractionsthe result will be finiteand displayed in full precision — regardless of the setting for the number of fractional bits.

Although this calculator implements pure binary arithmetic, you can use it to explore floating-point arithmetic. For example, say you wanted to know why, using IEEE double-precision binary floating-point binary division online remainder, There are two sources of imprecision in such a calculation: Decimal to floating-point conversion binary division online remainder inexactness because a decimal operand may not have an exact floating-point equivalent; limited-precision binary arithmetic introduces inexactness because a binary calculation may produce more bits than can be stored.

In these cases, rounding occurs. My decimal to binary converter will tell you that, in pure binary, To work through this example, you had to act like a computer, as tedious as that was. First, you had to convert the operands to binary, binary division online remainder them if necessary; then, you had to multiply them, and round the result.

For practical reasons, the size of the inputs — and the number of fractional bits in an infinite division result — is limited. If you exceed these limits, you will get an error message. But within these limits, all results will be accurate in the case of division, results are accurate through the truncated bit position. Skip to content Operand 1 Enter a binary number e.

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