Hexadecimal Calculator

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Hexadecimal Calculator

To use Hexadecimal Calculator, enter the values in the input boxes below and click on the Calculate button.


About Hexadecimal Calculator

Hexadecimal Calculator

To perform operations with hexadecimal numbers such as addition, subtraction, multiplication and division you can utilize this tool in hex calculator mode. Additionally you can use it in hex converter mode to convert a hexadecimal number to its decimal equivalent or vice versa (decimal to hex and hex to decimal conversion). Furthermore this tool allows you to convert hex numbers to binary numbers to hex.

What exactly is a hexadecimal number? It is a number expressed in the positional numeral system, which has a base of 16. This system uses sixteen symbols; the numbers from 0 to 9 and the letters A,B,C,D,E and F. These symbols represent values ranging from 0 to 15. Alternatively lowercase letters a through f can be used well. For instance the decimal value of 10 corresponds to A in notation; similarly 100 in decimal converts to 64 in hexadecimal notation; and finally 1,000 in decimal converts to 3E8 in hexadecimal notation. Just like numbers have signs (positive or negative) hex numbers also have signs. For example 1e is equal to 30 in notation.

Hexadecimal numerals find usage within computing fields such, as computer system design, software engineering and programming. These professionals often require the assistance of a hex calculator or hex converter.
You would come across these characters on a daily basis while browsing the internet. In website addresses (URLs) special characters are encoded using a numeral system. For example %20 represents a space or blank. Many webpages also encode characters in HTML by using their corresponding hexadecimal numerical character references, such as ’ for a single quotation mark (’). A regular person browsing the web shouldn't need to use a converter or calculator for this purpose.

With our hex calculator you can perform operations like addition, subtraction, multiplication and division on hexadecimal numbers. It also serves as a tool for converting between hex and decimal, decimal and hex, hex and binary as well, as binary and hex.

Below is a table that shows some numbers represented in the system (base 10) hex system (base 16) and binary system (base 2).

Decimal Hex Binary
0 0 0
1 1 1
2 2 10
3 3 11
5 5 101
10 A 1010
11 B 1011
12 C 1100
13 D 1101
14 E 1110
15 F 1111
50 32 110010
63 3F 111111
100 64 1100100
1000 3E8 1111101000
10000 2710 10011100010000


Converting between hexadecimal and decimal numerals

When converting numbers between hex and decimal the actual value of the number remains the only its representation changes. Our hex converter above allows you to easily perform both types of conversions. It's important to note that hex conversion and hex calculation are operations meaning you can do one without needing to do the other.

Hexadecimal to decimal

In a hexadecimal numeral each position represents a power of 16 to how each position in a decimal number represents a power of 10. For instance in notation the number 20 is equal to 2 x 101 + 0 times 100 resulting in 20. In notation the number 20 is equal to 2 x 161 + 0 x 160 resulting in a value of 32 in decimal form. Similarly the number 1E is equal to multiplying its digit (1) by sixteen raised to the power of one plus multiplying its second digit (E) by sixteen raised to the power of zero. This calculation yields a value of thirty in form.

To convert from hex to decimal you need to take each position and convert it individually; for example '9' remains as '9'. B' gets converted into '11'. Then multiply each position by sixteen raised to the power corresponding with its position number while counting from right (starting at zero). If you encounter exponents, like 168 our exponent calculator might come in handy.

Decimal to hexadecimal

This process becomes a bit more intricate when we transition from a numerical base to a lower one. Lets assume that the number we want to convert from decimal to hexadecimal is X. To begin we need to identify the power of 16 that is less than or equal to X, which we'll call E. Then determine how many times this power of 16 can be divided into X and assign that value as Z1. The remainder will be denoted as Y1.

Repeat these steps with Yn as the starting value until 16 is greater than the remaining value. Assign this remainder to the position representing 160. Assign each subsequent value from Y1...n to their respective positions until you have your hexadecimal representation.

Example conversion from decimal to hexadecimal; Lets convert 1000 in decimal to hexadecimal.

1) Largest power E = 2 (162 = 256 ≤ 1000, 163 = 4,096 ≥ 1000)

2) Z1 = 1000 / 162 = 3 (232 remainder); Y1 = 232

3) Largest power E = 1 (161 = 16 ≤ 232, 162 = 256 ≥ 232)

4) Z2 = 232 / 161 = 14 (8 remainder); Y2 = 8

5) 8 < 16; Z3 = 8, end.

To obtain the value of 3E8 (14 in decimal is equivalent to E in hexadecimal) you can confirm the outcome by using our converter.

Both hex to decimal and decimal to hex conversions follow principles but with a base of 2 instead of 10.

When performing operations with hexadecimal numbers using our tool in hexadecimal calculator mode you can carry out the four fundamental operations; addition, subtraction, multiplication and division. This means that it also functions as a calculator for adding and subtracting numbers. For numbers many individuals prefer to use a table for manual calculations while for larger ones a base 16 calculator is often utilized. Subtraction operates similarly to number systems; however when borrowing a digit you need to borrow a group of 1610 instead of 1010 as you would do with decimals.

Lets go through some examples to illustrate how hexadecimal arithmetic calculations work. First consider an addition; adding 4 (in hex) and F (, in hex). The sum is 3. There is a carry of 1 (since 19 = 16 +3). We prepend this carry to the sum of digits (3) resulting in the answer; 13.

For a complex addition example lets add the hex numbers 3F16 and 6416.Here is the step by step process for adding numbers in hexadecimal;

1) Start from the right. Add 416 to F16, which gives us 1316. We have 316 as the result. Carry over 116 to the left.
2) Next add 316 and 616. Don't forget to include the carryover of 116. The total sum is A16.
3) To get the result write down A316 by combining the outcomes of (2) and (1).
This is how addition works in hexadecimal. Other arithmetic operations in base 16 follow an approach, as their decimal counterparts.

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