Bitwise Calculator
AND, OR, XOR, NOT And Shifts

What A Bitwise Calculator Does For You

Computers store every number as bits, which are ones and zeros. Bitwise operations work on those bits one at a time. They are small, fast and everywhere in code.

But bits are hard to picture. A bitwise calculator fixes that. First, type two numbers. Then pick an operation. The bits line up in rows, so you see what changed.

Also, you can type numbers in decimal, hex, binary or octal. So you can paste a mask from a datasheet or a flag from code, and get the answer in any form.

Everything runs in your browser. So nothing you type leaves your device.

How Bitwise Operations Work

A bitwise operation lines up two numbers and compares them bit by bit. For AND, a result bit is 1 only when both bits are 1. For OR, it is 1 when at least one bit is 1. For XOR, it is 1 when the bits differ.

So 12 AND 10 gives 8. In binary, 1100 AND 1010 gives 1000.

For more detail, see: Wikipedia article on bitwise operations.

Bitwise AND

First, AND keeps only the bits that are set in both numbers. Use it to read a flag or to apply a mask. For example, a value AND 0xFF keeps the lowest eight bits.

Bitwise OR

OR sets a bit if either number has it set. Also, use it to switch a flag on, or to combine two masks into one.

Bitwise XOR

XOR sets a bit only when the two bits differ. Use it to flip bits, to compare two numbers, or to swap two values without a spare one. XOR with the same number twice gives back the start.

Then look at the bit rows in the tool. Each result bit sits under the two bits that made it.

NAND, NOR And XNOR

These three are the opposites of AND, OR and XOR. Each one runs the operation and then flips every bit. Chip designers love NAND and NOR, because either one can build every other gate.

Bitwise NOT

NOT flips every bit of one number. In 8 bits, NOT 0 gives 255. So the width matters, and you should pick it first. In 32 bits, NOT 0 gives 4294967295.

Shift Left

A left shift moves the bits toward the top and fills the gap with zeros. One step to the left doubles an unsigned number. So 3 shifted left by 2 gives 12.

Bits that fall off the top are lost. Then the tool shows what remains.

Shift Right: Logical And Arithmetic

A right shift moves the bits down. A logical shift fills the top with zeros. An arithmetic shift copies the top bit instead, so a negative number stays negative.

Then one step to the right halves a number and rounds down.

Rotate Left And Right

A rotate moves the bits like a shift, but the bits that fall off one end return at the other. So nothing is lost. Also, hashes and ciphers use rotates a lot.

Choose The Width

Pick 8, 16, 32 or 64 bits. The width sets how many bits NOT flips, where a shift loses bits, and how a number reads as signed.

A number too big for the width keeps only its lowest bits, and the tool tells you.

Signed And Unsigned Numbers

The same bits can mean two numbers. In 8 bits, 11111111 is 255 unsigned and -1 signed. The tool shows both, so you can pick the one your code uses.

Negative inputs use the standard two's complement form.

Type Numbers In Any Base

Choose decimal, hex, binary or octal for the box. You can also add a prefix, such as 0x for hex, 0b for binary and 0o for octal, and the prefix wins. Spaces and underscores do not count, so 1010 1111 works.

Common Uses

Programmers use bitwise operations for flags, masks, permissions, colour channels, packed data, hashes and fast maths. For example, a colour in 0xRRGGBB form keeps red in the top byte.

So shift right by 16 and AND with 0xFF to read it.

Check Your Code

Use the tool as a second opinion. Type the values from your code, run the same operation, and compare. So it helps you find an off by one shift or a wrong mask.

Safe By Design

First, the tool works in your browser. It sends nothing, and it stores nothing. So your numbers stay yours.