Hex calculator

Arithmetic and bitwise operations on hexadecimal numbers, with 64-bit signed or unsigned semantics — the same rules a CPU (and the HexCalculator iOS app) follows. Results appear in hex, decimal and binary as you type.

What this calculator does

Arithmetic: addition, subtraction, multiplication and division (truncated, like integer division in C or Swift).
Bitwise: AND, OR, XOR, left shift and right shift. Shifts accept amounts from 0 to 63; in signed mode right shift is arithmetic (the sign bit is preserved), in unsigned mode it's logical.
Signed mode works on 64-bit two's complement integers (−2⁶³ to 2⁶³−1). Unsigned mode covers 0 to 2⁶⁴−1.
Overflow and division by zero are reported, not silently wrapped — you'll see an error instead of a wrong number.

Why hex arithmetic trips people up

Adding hex numbers by hand means carrying at 16 instead of 10 — 0x8 + 0x9 = 0x11, not 0x17. Multiplication and division get worse. In practice nobody does this on paper: you use a programmer's calculator that keeps the base straight for you and shows the same value in decimal and binary, so you can sanity-check against whatever your debugger or datasheet says.

Hex addition, subtraction and multiplication by hand

The rules are the decimal ones with a carry at sixteen instead of ten. Adding 0x1A + 0x2C: A (10) + C (12) = 22, which is 16 + 6, so write 6 and carry 1; then 1 + 2 + 1 = 4. Result 0x46 (26 + 44 = 70, check).

0x1A + 0x2C = 0x46 · 0xFF + 0x01 = 0x100 · 0x100 − 0x01 = 0xFF

Subtraction borrows sixteen: 0x100 − 0x01 borrows down through both zeros to give 0xFF. Multiplication by a power of 16 just appends zeros (0x10 × 0x10 = 0x100), and multiplying by 2 is a one-bit left shift (0x7F × 2 = 0xFE). The calculator above shows every result in hex, decimal and binary so you can check each step; for AND, OR and XOR laid out bit by bit, use the bitwise calculator.

Related tools and guides

Bitwise calculator — AND, OR, XOR, NOT and shifts, shown bit by bit.
Integer ranges and powers of two — where 64-bit signed and unsigned arithmetic overflows.
Hex ↔ decimal converter — when you just need the value, with steps.
Bitwise operations explained — what AND, OR, XOR and shifts actually do.
Two's complement calculator — how the signed mode represents negatives.