Hexadecimal Calculator - Operations
Add, subtract, and multiply hexadecimal numbers, with the result converted to decimal and binary alongside the hex value.
Hexadecimal Calculator - Operations
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Formula: Hexadecimal: base-16 (0-9, A-F)
Worked example — 0xFF + 0x0A = 0x109 (265 in decimal)
Formula
Hexadecimal: base-16 (0-9, A-F)
Perform arithmetic on hexadecimal numbers. Convert between hex, decimal, and binary.
Worked Examples
Example 1: Hex addition that overflows a byte
Problem:0xFF + 0x0A
Solution:0xFF = 15 x 16 + 15 = 255, the largest value one byte holds. 0x0A = 10. 255 + 10 = 265. Back to hex: 265 = 1 x 256 + 0 x 16 + 9, so 265 = 0x109. The result needs three hex digits, so it no longer fits in a single byte.
Result:0xFF + 0x0A = 0x109 (265 in decimal)
Example 2: Hex multiplication and the binary shortcut
Problem:0x2C x 0x3
Solution:0x2C = 2 x 16 + 12 = 44. 44 x 3 = 132. 132 = 8 x 16 + 4, so the answer is 0x84. Each hex digit is exactly four bits, so 0x84 reads straight off as 1000 0100 in binary. Check: 1000 0100 = 128 + 4 = 132.
Result:0x2C x 0x3 = 0x84 (132 decimal, 1000 0100 binary)
Frequently Asked Questions
Why is hexadecimal used in computing?
Each hex digit represents exactly 4 bits, making it a compact way to represent binary data. 0xFF = 11111111 = 255.
How do I convert a hex number to decimal?
Multiply each digit by 16 raised to its positional power, then sum. For 0x1A: (1×16) + (10×1) = 16 + 10 = 26. Letters A-F represent decimal values 10-15 respectively.
Where is hexadecimal used in everyday programming?
Hex appears in HTML/CSS color codes (#FF5733), memory addresses in debuggers, MAC addresses (e.g., 00:1A:2B:3C:4D:5E), Unicode code points (U+1F600), and binary file inspection. It makes large binary values readable at a glance.
When would I use Hexadecimal Calculator - Operations?
Use it when debugging memory dumps, converting color values between formats, calculating bitmasks for hardware registers, or verifying network protocol fields that are commonly expressed in hexadecimal notation.
How do I add hexadecimal digits by hand?
Add column by column exactly as in decimal, but carry whenever a column reaches 16 rather than 10. So 0x9 + 0x8 is 17, which is one carry plus 1, written 0x11. Adding 0xA and 0x7 gives 17 as well, again 0x11. It helps to keep the letter values in mind: A is 10, B is 11, C is 12, D is 13, E is 14 and F is 15. Subtraction borrows 16 from the next column instead of 10.
How do I convert a hexadecimal number straight to binary?
Replace each hex digit with its own four-bit group, keeping the order. 0x2F becomes 0010 followed by 1111, so 0x2F is 00101111, or 47 in decimal. No intermediate decimal step is needed, because one hex digit maps onto exactly one nibble. The same shortcut runs backwards: split a binary string into fours from the right and read each group as a hex digit. Hexadecimal Calculator - Operations shows the binary form of every result for that reason.
What do the prefixes 0x and # and the trailing h mean?
They are all notations for the same thing, marking a literal as base 16 so it is not misread as decimal. 0x is the C, Java and JavaScript convention and is what Hexadecimal Calculator - Operations echoes. The hash prefix is used for colour literals in CSS and HTML. A trailing h, as in 1Ah, is the traditional assembler style, and some assemblers also use a $ prefix. None of them changes the value, only how the parser recognises it.
How are negative values shown, and how would hardware store them?
If a subtraction here yields a negative number the minus sign lands inside the digits rather than in front of the prefix, so 0xA minus 0xF prints as 0x-5 and its binary line reads -101; read that as minus five. A fixed-width register would instead hold the two's complement pattern, so -5 in a single byte is 0xFB and -1 is 0xFF. That is why a memory dump full of 0xFF bytes often means small negative numbers or an erased flash region rather than a genuinely huge value.
Why is 0xFF the largest value that fits in one byte?
A byte is eight bits and each hex digit covers four bits, so exactly two hex digits describe a byte. The largest two-digit hex number is FF, which is 15 x 16 + 15 = 255, and with zero included that gives the 256 distinct states of eight bits. This is why byte-oriented quantities such as colour channels, IPv4 octets and unsigned char variables all top out at 255, and why hex dumps are laid out in pairs of digits.
What is the difference between big-endian and little-endian in a hex dump?
Endianness is the order in which the bytes of a multi-byte value are laid out in memory. A big-endian machine stores the 32-bit value 0x12345678 as the byte sequence 12 34 56 78, matching how you write it. A little-endian machine, which includes x86 and most ARM configurations, stores it as 78 56 34 12. Reading a dump with the wrong assumption reverses your number entirely, so it is the first thing to check when a parsed field looks nonsensical.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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