Free Hex Calculator Online
Perform hexadecimal arithmetic (+, −, ×, ÷) and bitwise operations (AND, OR, XOR, NOT, Shifts) with simultaneous Decimal, Binary, and Octal conversions.
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Understanding Hexadecimal Mathematics & Bitwise Computing
The hexadecimal number system (Base 16) is a core pillar of computer architecture, systems programming, and digital cryptography. Unlike our standard Base 10 decimal system that uses ten symbols (0–9), hexadecimal utilizes sixteen distinct symbols: numbers 0 through 9, followed by the letters A, B, C, D, E, and F (representing values 10 through 15).
Computers operate fundamentally on binary switches (0 and 1). However, reading long 32-bit or 64-bit strings of binary is difficult for humans. Because 16 = 2^4, exactly four binary bits (a nibble) map to one single hexadecimal character (e.g. binary 1111 = hex F). This mathematical harmony makes hex the universal shorthand for memory addresses, color hex codes (#FFFFFF), machine bytecode, and IPv6 networking.
Hexadecimal Calculation Rules & Operations
Hex Addition & Carrying
Just like decimal additions carry over when sums reach 10, hex addition carries over when sums reach 16 (0x10). For example, 8 + 8 = 10 (16 in decimal), and F + 1 = 10.
Hex Subtraction & Borrowing
When subtracting a larger digit from a smaller one, you borrow 16 from the higher order digit. For example, 10 - 1 = F, and 100 - 1 = FF.
Bitwise Logic (AND, OR, XOR)
Bitwise operations compare each binary bit: AND keeps only bits set to 1 in both inputs, OR keeps bits set in either, and XOR flips bits that differ (frequently used in crypto hashes).
Bit Shifts (<< and >>)
Shifting left by 1 bit multiplies the integer value by 2 (or by 16 when shifting 4 bits). Shifting right divides the value, forming the basis of ultra-fast arithmetic in assembly code.
Hex to Decimal & Binary Reference Chart
| Hex | Dec | Binary | Hex | Dec | Binary | Hex | Dec | Binary | Hex | Dec | Binary |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0 | 0000 | 4 | 4 | 0100 | 8 | 8 | 1000 | C | 12 | 1100 |
| 1 | 1 | 0001 | 5 | 5 | 0101 | 9 | 9 | 1001 | D | 13 | 1101 |
| 2 | 2 | 0010 | 6 | 6 | 0110 | A | 10 | 1010 | E | 14 | 1110 |
| 3 | 3 | 0011 | 7 | 7 | 0111 | B | 11 | 1011 | F | 15 | 1111 |
Frequently Asked Questions (FAQ)
0xFF + 0x01 causes an integer overflow and rolls over to 0x00. Selecting a bit width simulates real CPU register architectures.