About

Debugging low-level code often involves manual memory management or analyzing binary dumps. Programmers frequently need to calculate offsets, determine jump addresses, or align data structures in memory. These tasks require thinking in base-16 rather than the standard base-10 used by everyday calculators. Errors in these calculations lead to segmentation faults or buffer overflows.

This tool performs arithmetic directly on hexadecimal strings. It utilizes 64-bit integer logic to handle large values typically found in memory addresses (pointers). Unlike standard floating-point calculators which lose precision at high values, this calculator maintains integer integrity. It provides simultaneous output in decimal and binary formats. This helps developers visualize the bitwise consequences of arithmetic operations immediately.

Formulas

Hexadecimal arithmetic follows the same positional logic as decimal arithmetic but operates with a radix of 16. The digits extend from 0 to 9 and A (10) through F (15). When a column sum exceeds 15 (F), a carry is propagated to the next position.

Example Addition:

1A+F = 29

Logic breakdown:

Step 1: A (10) + F (15) = 25
Step 2: 25 in Hex is 19 (since 16 × 1 + 9)
Step 3: Keep 9 and carry 1
Step 4: 1 (from 1A) + 1 (carry) = 2
Result: 29

Conversion Formula:

The value of a hex string h_n...h₀ is:

V = n∑i=0 h_i ⋅ 16ⁱ

Reference Data

Hexadecimal (Base 16)	Decimal (Base 10)	Binary (Base 2)	Note / Common Use
0x0	0	0000	Null / Zero
0x1	1	0001	Bit 0 Set
0xA	10	1010	Decimal 10
0xF	15	1111	Max 4-bit (Nibble)
0x10	16	0001 0000	$16^1$
0xFF	255	1111 1111	Max 8-bit (Byte)
0x100	256	1 0000 0000	$16^2$
0xFFFF	65535	1111...	Max 16-bit (Short)
0x7FFFFFFF	2147483647	0111...	Max Signed 32-bit
0xFFFFFFFF	4294967295	1111...	Max Unsigned 32-bit
0xDEADBEEF	3735928559	...	Debug Magic Value
0xFFFFFFFFFFFFFFFF	18446744073709551615	...	Max Unsigned 64-bit

Frequently Asked Questions

This calculator performs mathematical arithmetic. If you subtract a larger number from a smaller one, the result will be a negative signed hex (e.g., -0x5). In computer memory, this is typically stored using Two's Complement representation.

This tool uses 64-bit integer precision (BigInt). It can handle values up to 2^63 - 1 for signed operations and display much larger numbers without losing the least significant bits, unlike standard JavaScript number types.

In Base-16 (Hexadecimal), the "1" in the second position represents 16 to the power of 1. Just as "10" in Base-10 means 1 ten and 0 ones, "10" in Base-16 means 1 sixteen and 0 ones.

Yes. This is the primary use case. You can add a decimal offset to a hex base address or subtract two hex addresses to find the size of a data block in bytes.

Division by zero is mathematically undefined. The calculator will return "Infinity" or an error state depending on the context, rather than crashing.