Bitwise Calculator

Bitwise Calculator applies AND, OR, XOR, NOT and the two shift operations to numbers at a fixed register width, and shows the bit pattern at every step. Seeing the bits lined up is the point: bitwise operations are column arithmetic, and once the columns are visible the result stops being mysterious.

Width is a genuine input, not a display choice. AND, OR and XOR give the same answer at any width, but NOT and the shifts do not: ~202 is 53 in eight bits and 4,294,967,093 in thirty-two, because NOT flips every bit in the register and a wider register has more bits to flip. A left shift past the top of the register loses those bits entirely. Choose the width your language or protocol actually uses and the answer will match it.

These operations are the basis of flags and masks. AND with a mask tests or clears bits, OR sets them, XOR toggles them, and a shift moves a value into position within a packed field. Permission bits, network masks, hardware registers and compression formats are all built from exactly these five operations, which is why the comparison rows show AND, OR and XOR together.

The page shows its working, not just its answer. Where there is a formula it is printed with your own numbers substituted in, so you can check the result rather than take it on trust -- which is the difference between a calculator you can use for something that matters and one you cannot.

Everything runs inside your browser. What you type is never uploaded, never logged and never stored, and the calculator keeps working if your connection drops after the page has loaded.

• Shows result, result in bits, in hexadecimal, bits set and as a signed value together, so you are not running it twice
• A results table you can read across
• Prints the formula with your own figures substituted in
• Updates as you type, with no button to press and no page reload
• Copy the result in one click
• Free, no sign-up, and it runs entirely in your browser

The bitwise calculator is used by writers, developers, students, marketers and anyone else who needs the job done once without installing software. Common cases include:

• Testing or setting flag bits with a mask
• Checking what a shift does to a value
• Working out a permissions or register value
• Debugging a packed binary field