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.

Because every operand and result is displayed in all four bases, the same page is a binary math calculator and a base converter. Set the input base to decimal and add 200 and 55: the answer 255 appears as 11111111 in binary and FF in hex. That covers the decimal to binary calculator and binary to hexadecimal calculator jobs without opening a separate tool, and to convert a single number you can simply add 0 to it.

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.