255
16
271
239
4,080
0
0
239
15
15
0
0
0
4,080
16
16
16
16
255
16
271
239
4,080
0
0
239
15
15
0
0
0
4,080
16
16
16
16
The Hexadecimal Calculator performs arithmetic operations on decimal numbers and displays the results along with hexadecimal digit breakdowns. It supports addition, subtraction, multiplication, division, and modulo operations, making it a versatile tool for programmers, computer scientists, and digital electronics engineers.
Hexadecimal (base-16) is one of the most important number systems in computing. It uses sixteen symbols: 0–9 for values zero through nine, and A–F for values ten through fifteen (displayed as 10–15 in this calculator’s digit outputs). Each hexadecimal digit represents exactly four binary bits (a nibble), which is why hex became the preferred compact representation for binary data.
Hexadecimal arithmetic is used extensively in programming and computer engineering. Memory addresses are displayed in hex (0x7FFE1234), color codes in web development use hex (#FF5733 = Red:255, Green:87, Blue:51), MAC addresses use hex (00:1A:2B:3C:4D:5E), Unicode code points are expressed in hex (U+00E9 for é), and assembly language instructions use hex operands throughout.
Hex addition follows the same column-by-column rules as decimal addition, but carries occur at 16 instead of 10. For example, adding hex A (10) + hex 7 (7) = 17 decimal = hex 11 (1 carry, 1 remainder). Learning hex arithmetic helps you work with raw binary data, debug memory dumps, calculate address offsets, and understand how CPUs handle data at the register level.
The modulo operation (remainder after division) is particularly useful in programming for tasks like hash table indexing, circular buffer management, checking divisibility, and generating cyclic patterns. In hexadecimal contexts, modulo 16 extracts the least significant hex digit, modulo 256 extracts the least significant byte, and so on.
This calculator displays the hexadecimal digit decomposition of both the first input and the result. Each digit position represents a power of 16: the ones place (160 = 1), sixteens place (161 = 16), two-fifty-sixes place (162 = 256), and four-thousand-ninety-sixes place (163 = 4096). Values 10–15 in these positions correspond to hex letters A–F.
Whether you are computing memory offsets, manipulating pixel colors, working with network byte order, or simply learning hexadecimal, this calculator provides both the decimal result and a positional hex breakdown to deepen your understanding of base-16 arithmetic.
For related tools, see the Programmer Calculator for base conversion and the Bitwise Calculator for logical operations on binary data.
Hexadecimal arithmetic operations follow standard positional arithmetic rules with base 16:
Hex Addition: Add corresponding hex digits. If the sum ≥ 16, write sum − 16 and carry 1 to the next position.
$$\text{If } a_i + b_i + c_i \ge 16: \quad d_i = (a_i+b_i+c_i) - 16, \quad c_{i+1} = 1$$
Hex Subtraction: Subtract corresponding digits. If the result is negative, borrow 16 from the next position.
Hex Digit Extraction from a decimal number \(N\):
$$h_k = \left\lfloor \frac{N}{16^k} \right\rfloor \mod 16$$
where \(h_k\) is the hex digit at position \(k\) (0-indexed from least significant). Values 10-15 correspond to hex digits A-F.
Modulo (remainder):
$$A \mod B = A - \left\lfloor \frac{A}{B} \right\rfloor \times B$$
The Result shows the decimal output of the operation. For division, up to 6 decimal places are shown. The Hex Digit outputs show the positional breakdown of both input A and the result in hexadecimal. Each digit value ranges from 0–15, where 10=A, 11=B, 12=C, 13=D, 14=E, 15=F. For example, if Result Hex Digit 1 = 15 and Digit 2 = 15, the hex representation is FF (255 decimal). Division by zero and modulo by zero return 0 for safety.
Inputs
Results
255 + 16 = 271 decimal. In hex: FF + 10 = 10F. The result hex digits are F(15), 0, 1 from least to most significant.
Inputs
Results
500 mod 256 = 244 decimal = F4 hex. This extracts the value within a single byte (0-255 range).
Hexadecimal (hex) is a base-16 number system using digits 0-9 and letters A-F (representing 10-15). Each hex digit corresponds to exactly 4 binary bits, making hex a convenient compact representation of binary data used throughout computing.
Hex is compact (8 hex digits represent a 32-bit value vs. 32 binary digits), easy to convert to/from binary (each hex digit = 4 bits), and is the standard for memory addresses, color codes, network data, character encodings, and low-level debugging.
HTML/CSS colors like #FF5733 use three hex byte pairs: Red=FF(255), Green=57(87), Blue=33(51). #000000 is black (all zero), #FFFFFF is white (all max). Each component ranges from 00 to FF (0-255 decimal).
Add column by column from right to left, using hex digit values (A=10, B=11, etc.). If a column sum is 16 or greater, subtract 16 and carry 1 to the next column. For example: hex 8 + hex A = 18 decimal = 12 hex (write 2, carry 1).
The 0x prefix (e.g., 0xFF) is a common notation in programming languages (C, C++, Java, Python, JavaScript) to indicate a hexadecimal literal. It distinguishes hex from decimal: 0x10 = 16 decimal, not 10. Some languages use $ or # instead.
Each hex digit maps to exactly 4 binary bits: 0=0000, 1=0001, ..., 9=1001, A=1010, B=1011, C=1100, D=1101, E=1110, F=1111. This bijection makes conversion trivial: group binary digits by fours and replace each group with its hex equivalent.
Computer memory addresses are typically displayed in hexadecimal (e.g., 0x7FFF5FBFF8A0). Hex makes it easy to identify byte boundaries, page boundaries (often at multiples of 0x1000 = 4096), and segment offsets in memory layout analysis.
Hex modulo extracts lower-order digits/bytes. Mod 16 gives the last hex digit, mod 256 gives the last byte, mod 65536 gives the last two bytes. This is used in hash functions, cyclic buffers, byte-level data extraction, and checksum calculations.
MAC addresses like 00:1A:2B:3C:4D:5E consist of 6 hex byte pairs (48 bits total). The first 3 bytes identify the manufacturer (OUI), and the last 3 are a unique device identifier. Hex notation makes each byte clearly readable.
Unicode code points are written in hexadecimal (U+0041 = A, U+00E9 = e with accent, U+1F600 = smiley emoji). UTF-8, UTF-16, and other encodings are also typically discussed using hex byte values for clarity.
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