Hexadecimal Calculation—Add, Subtract, Multiply, or Divide
Convert Hexadecimal Value to Decimal Value
Convert Decimal Value to Hexadecimal Value
Hex Calculator: Ultimate Guide to Hexadecimal Arithmetic
Hex Calculator tools simplify operations on hexadecimal numbers, a system widely used in computing and digital electronics—from memory addresses to color codes in HTML—due to its compact representation relative to binary and decimal systems. Whether you need a hex converter, a hex addition calculator, or a hex subtraction calculator, understanding the underlying manual processes ensures you can verify results and deepen your comprehension of base‑16 arithmetic.
Understanding the Hexadecimal System
Hexadecimal is a positional numeral system with a base of 16, using sixteen distinct symbols: 0–9 to represent values zero to nine, and A–F to represent values ten to fifteen. Each digit’s place value corresponds to a power of 16, much like decimal places correspond to powers of 10. For example, the hex number 2F7 equals 2×16² + 15×16¹ + 7×16⁰ = 759 in decimal.
Manual Hex Calculations
Hex to Decimal Conversion: Step‑by‑Step
To perform a How to convert hex to decimal step‑by‑step calculator process manually:
Break the hex number into individual digits.
Map each digit to its decimal equivalent (A = 10 through F = 15).
Multiply each digit by 16 raised to the power of its position index, counting from the rightmost digit as position zero.
Sum all the products.
Example: Convert 3A9₁₆ to decimal:
3×16² = 3×256 = 768
A(10)×16¹ = 10×16 = 160
9×16⁰ = 9×1 = 9
Total = 768 + 160 + 9 = 937₁₀
| Decimal | Binary | Hexadecimal |
|---|---|---|
| 0 | 00000 | 0 |
| 1 | 00001 | 1 |
| 2 | 00010 | 2 |
| 3 | 00011 | 3 |
| 4 | 00100 | 4 |
| 5 | 00101 | 5 |
| 6 | 00110 | 6 |
| 7 | 00111 | 7 |
| 8 | 01000 | 8 |
| 9 | 01001 | 9 |
| 10 | 01010 | A |
| 11 | 01011 | B |
| 12 | 01100 | C |
| 13 | 01101 | D |
| 14 | 01110 | E |
| 15 | 01111 | F |
| 16 | 10000 | 10 |
| 17 | 10001 | 11 |
| 18 | 10010 | 12 |
| 19 | 10011 | 13 |
| 20 | 10100 | 14 |
Hex Addition with Carry Explanation
A Hex addition calculator with carry explanation follows these rules:
Align numbers by the least significant digit.
Add corresponding digits.
If the sum ≥ 16, subtract 16 to get the digit and carry 1 to the next column.
Example: Add 9D₁₆ + 4B₁₆:
Units: D(13) + B(11) = 24; 24–16 = 8, carry 1.
Sixteens: 9 + 4 + carry 1 = 14 ⇒ E.
Result:
E8₁₆ (232₁₀).
Hex Subtraction Fundamentals
To understand hex subtraction manually or using a How to subtract hex numbers using a calculator:
Align numbers.
Subtract digits; if the top digit is smaller than the bottom, borrow 1 (worth 16) from the next column.
Adjust the current column: add 16 to the top digit before subtraction.
Example: Subtract 5A₁₆ – 2F₁₆:
Units: A(10) < F(15), borrow 1 ⇒ (10+16)=26; 26–15=11 (B), next column loses 1.
Sixteens: 5–1 (borrow) – 2 = 2 ⇒ 2.
Result:
2B₁₆.
Hex Multiplication Process
Hexadecimal multiplication mirrors decimal multiplication:
Multiply each digit of one number by each digit of the other, starting from the least significant digits.
Record the product and any carry (over values ≥ 16).
Shift partial products by position and sum them.
Example: Multiply A6₁₆ × 1C₁₆:
A(10)×C(12) = 120; 120 ÷16 = 7 remainder 8 ⇒ write 8 carry 7.
6×C + carry 7 = 6×12 +7 = 79; 79 ÷16 = 4 remainder 15 (F).
Repeat for ×1 and shift.
Final:
C60₁₆ (3168₁₀).
Hex Division Explained
Long division in hex employs repeated subtraction of (divisor×quotient digit) from the dividend:
Position the dividend under a division bracket, divisor outside.
Determine how many times the divisor fits into the leading hex digits of the dividend.
Multiply divisor by that quotient digit, subtract, bring down next digit.
Continue until all digits are processed.
Example: Divide E4D₁₆ by A₁₆:
A(10) into E(14): fits 1 time (1×A=10); subtract → remainder 4.
Bring down 4 → 44 (hex) → fits 4 times (4×A=40); subtract → remainder 4.
Bring down D → 4D → fits 4 times (4×A=40); remainder D.
Quotient:
144₁₆, Remainder: D (13₁₀).
Using a Hex Calculator for Programming
In software development and debugging, How to use a hex calculator for programming is indispensable. Programming languages and hardware interfaces often present data in hex (e.g., memory addresses, color codes). A hex calculator lets programmers quickly:
Convert between hex and decimal to interpret values.
Perform arithmetic on pointers, offsets, and masks.
Validate manual calculations to prevent subtle bugs in low‑level code.
Modern hex calculators also support bitwise operations (AND, OR, XOR), lookup of two’s complement representations, and toggling between upper/lowercase hex digits—features that streamline embedded systems coding and reverse engineering.
Key Features of Our Hex Calculator
Our Hex Calculator’s user‑friendly interface and powerful capabilities make it the go‑to hex converter and hex calculator for both learners and professionals. It seamlessly performs hex addition, hex subtraction, hex multiplication, and hex division, providing decimal equivalents alongside your hex results for easy verification.
Features: allows user to do addition, subtraction, multiplication and division of hex numbers and also give its decimal equivalent; allows to convert hex to decimal and decimal to hex.
