Bitwise calculator

Compute AND, OR, XOR, NOT, NAND, NOR, XNOR and left/right shifts on two numbers. Enter values in decimal, hexadecimal (0x), or binary (0b) at 8, 16, or 32 bits, and see the result in binary, decimal, and hex, plus a per-bit breakdown that shows each operation is a logic gate applied column by column. For example, 12 ^ 10 = 6 (that is 1100 XOR 1010 = 0110).

How to use it

Type a number into A (and B for the two-input operations), pick an operation, and choose a bit width. Numbers can be plain decimal, hexadecimal with a 0x prefix, or binary with a 0b prefix, and a negative decimal is folded into its two's-complement pattern at the chosen width. The result updates as you type, shown in all three bases with a bit-by-bit table lining up A, B, and the output so you can see exactly which columns changed.

Worked example: 12 XOR 10

Write both numbers in binary: 12 is 1100 and 10 is 1010. XOR outputs a 1 wherever the two bits differ. Comparing column by column: the top bits are 1 and 1 (same, 0), the next are 1 and 0 (differ, 1), then 0 and 1 (differ, 1), then 0 and 0 (same, 0). The result is 0110, which is 6. That is exactly what four XOR gates in parallel would produce.

The operations

AND (&) gives 1 only where both bits are 1, the standard way to mask bits. OR (|) gives 1 where either bit is 1, used to set bits. XOR (^) gives 1 where the bits differ, used to toggle bits and to compare. NOT (~) flips every bit of a single number. NAND, NOR and XNOR are the inverted forms. A left shift (<<) multiplies by two per position and a right shift (>>) divides by two.

Bitwise operators are logic gates

The point worth internalizing: a bitwise operator is nothing more than a logic gate wired up once per bit. When a CPU computes a & b on two 8-bit numbers, it runs eight AND gates in parallel, one per bit column, exactly like the table above. Build one of those gates from transistors in the lab, then line eight of them up, and you have built the AND instruction. Read the boolean algebra behind it, or see it in a real ALU.

Frequently asked

What is a bitwise XOR?

Bitwise XOR (exclusive OR, written ^) compares two numbers bit by bit and outputs a 1 in each position where the two bits differ, and 0 where they are the same. For 12 ^ 10: 1100 XOR 1010 = 0110, which is 6. It is the same operation an XOR gate performs, applied to every bit column at once.

What does bitwise AND do?

Bitwise AND (written &) outputs a 1 in a bit position only when both input bits are 1. For 12 & 10: 1100 AND 1010 = 1000, which is 8. It is commonly used to mask bits, keeping only the positions where the mask has a 1.

How do left and right shift work?

A left shift (<<) moves every bit toward the high end, filling with zeros on the right, which multiplies the value by 2 per shift. A right shift (>>) moves bits toward the low end, dividing by 2 and discarding the bits that fall off the right.

What is the difference between bitwise operators and logic gates?

There is none, really: a bitwise operator is a logic gate applied to every bit of two numbers at once. AND, OR, XOR and NOT on numbers are the exact same gates you can build from transistors, wired one per bit position.