Binary Calculator

A binary calculator performs arithmetic and bitwise operations on integers written in base two. Enter two numbers, choose an operation such as add, subtract, multiply, divide, AND, OR, XOR, or a bit shift, and the tool returns the answer with every step shown in binary, octal, decimal, and hexadecimal at once. You are not limited to base two either: switch the input base and you can add a hex value to another hex value, or XOR two decimal numbers, without converting anything by hand first.

Two families of operations behave differently, and the tool keeps them separate. Arithmetic (add, subtract, multiply, divide, modulo) works on the true mathematical value, so it is exact no matter how many digits you enter and division reports the integer quotient along with any remainder. Bitwise operations (AND, OR, XOR, NAND, NOR, XNOR, NOT, and left and right shifts) act on the raw bit pattern inside a fixed register, so they depend on a chosen width. That is why the tool lets you pick 8, 16, 32, or 64 bits: NOT of a number, or a shift that pushes bits off the end, only has a defined answer once you know how wide the register is, exactly as in C, Java, Go, or Rust.

Fixed-width bitwise results are shown using two's-complement, the representation nearly every processor uses for signed integers. When a bitwise result has its top bit set, the tool reports both the unsigned reading and the signed reading, so you can see why ~5 becomes 250 in eight unsigned bits but −6 when the same bits are read as signed. Everything runs in your browser using JavaScript BigInt, so values never overflow silently and nothing you enter is uploaded, logged, or stored. The calculator keeps working with your network disconnected once the page has loaded.