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Calculator for calculating in hexadecimal, including addition, subtraction, multiplication, and division
Convert Hexadecimal Value to Decimal Value
Convert Decimal Value to Hexadecimal Value
The hexadecimal number system, sometimes known as hex, is extremely similar to both the binary and decimal systems in terms of how it operates. It does not use a base of 10, nor does it use a base of 2, but rather it uses a base of 16.
The hexadecimal system is similar to the decimal system in that it employs 16 digits, but in addition to the numerals 0-9, it also uses the letters A, B, C, D, E, and F (which are identical to a, b, c, d, and f) to represent the numbers 10-15.
It is easier to write large binary numbers using hexadecimal notation because each hex digit is equivalent to four binary digits, often known as nibbles. As an illustration, the value 1010101010 in binary can be converted into the hexadecimal representation 2AA.
This enables computers to compress huge binary values in a manner that facilitates a straightforward transition between the two coding methods.
The following are some common conversions that can be made between binary, hexadecimal, and decimal values:
Understanding the place values of each of the distinct number systems is required in order to convert between decimal and hexadecimal. On the page dedicated to binary calculators, you'll find a more comprehensive discussion.
It is important to keep in mind that the process of converting between decimal and hex is relatively comparable to the process of converting between decimal and binary. If either can be converted, then the process of doing so for the other should be rather straightforward.
As was explained earlier, hex operations are performed using the base of 16. This indicates that each place value, in the case of the value 2AA, corresponds to a power of 16. Beginning from the right, the first "A" denotes the "ones" location, which is equivalent to the number 160.
The number 161 is represented by the second "A" from the right, and the number 162 is represented by the 2. Keep in mind that the value "A" in hexadecimal is equal to the value "10." After acquiring this knowledge, it will be possible to convert from hexadecimal to decimal, as will be demonstrated below:
EX:2AA = (2 × 162) + (A × 161) + (A × 160)= (2 × 256) + (10 × 16) + (10 × 1)= 512 + 160 + 10 = 682
The conversion from decimal to hexadecimal is significantly more complicated, but it uses the same fundamental ideas. Please refer to the instructions and examples that are listed below. In order to have an understanding of the process, it is essential to work through the example that has been supplied in conjunction with the steps that have been listed:
Find the highest power of 16 that is lower than or equal to the number that has to be converted (we'll refer to it as X for the rest of this discussion).
Determine the number of times the power of 16 discovered in Step 1 goes into X, and make a note of that result.
The answer can be reached by multiplying the number discovered in Step 2 by the power of 16, and then deducting this result from X. The new value will be denoted with the letter Y going forward.
It is important to take note that the value entered in the place value for the power of 16 that was found will be the number that was found in Step 2.
The hex value would have the number 3 in its 164 place value if, for example, the highest power of 16 was discovered to be 164 and the number found in Step 2 was 3. In this scenario, the hex value would be written as 3qrst, where qrst represents the 160 through 3 place values.
Repeat Steps 1 through 3 with Y serving as the new starting value each time. Carry on with the process until the value that is left is less than or equal to 16, and then assign the value that is left to the place value of 160.
In order to calculate the hexadecimal value, you must first assign each of the values that were discovered after each repetition of Step 2 to the appropriate place value.
EX:Convert decimal 1500 to hex (1)
The greatest power is 162, which equals 256. (2)
256 × 5 = 1280, so (5 × 162)(3) (3)
1500 - 1280 = 220(4) (4)
16 × 13 = 208, so (13 × 161)
220 - 208 = 12(6) (6)
Since 16 is more than 12, the value in the 160s place value is the number 12.
1500 = (5 × 162) + (13 × 161) + (12 × 160)
Keep in mind that the numbers 10-15 are written out in letters. In hex: 13 = D, and 12 = C (9) Therefore, the hexadecimal representation of the number 1500 is: 5DC
The conversion from hexadecimal to decimal uses the same fundamentals but is often considered to be less complicated.
Find the total of each of the individual results after multiplying each digit in the hex value by the place value that corresponds to it. It makes no difference to the procedure whether or not the hex value comprises letter numbers; everything remains the same.
EX:Convert hex 1024 to decimal(1)(1 × 163) + (0 × 162) + (2 × 161) + (4 × 160)(2)4096 + 0 + 32 + 4 = 4132
The only difference between hex addition and decimal addition is the addition of the numerals A, B, C, D, E, and F. Hex addition follows the same rules as decimal addition. When executing hex operations, it may be helpful to have the decimal equivalent values of A through F ready, especially if the values have not yet been committed to memory.
An illustration of hex addition can be found below. Follow through with the example, and if you need any extra clarification, look to the text that is located underneath it.
Calculating hex addition is similar to doing simple decimal addition, but it also requires translating between hex and decimal when dealing with quantities that are more than nine (the numerals A through F).
In the previous illustration, B plus 8 is represented in decimal as 11 plus 8, which equals 19. 19 in decimal translates to 13 in hex since there is only one set of 16 digits and there are three extras. The value one is carried over to the next column, just like it does in decimal addition.
Because of this, the calculation for the next column is 1 plus A ten plus seven, which equals 18 in decimal or 12 in hex. Carry the 1 over to the last column, which will result in 1 + 8 + B (11) = 20 in decimal or 14 in hexadecimal. This gives us the hexadecimal value of 1423.
The process of computing hex subtraction is quite similar to that of computing hex addition; the process involves performing the operation while converting between hexadecimal and decimal values. The concept of borrowing represents the primary distinction between hexadecimal subtraction and decimal subtraction. When you borrow in hex, the "1" that you do so reflects 16 decimal rather than the 10 decimal that you would expect.
This is due to the fact that the column being borrowed from is sixteen times larger than the column that is being borrowed from (the same reason that the borrowed 1 in decimal represents 10). Hexadecimal subtraction is not more difficult than decimal subtraction as long as this fact is taken into consideration and careful attention is paid to the conversions of the letter numerals A through F.
Follow through with the example, and if you need any extra clarification, look to the text that is located underneath it.
In the first column on the right of the preceding example, C, which represents a value of 12 decimal, is less than F, which represents a value of 15 decimal. As a result, it is essential to take something from the column to the right. As a result, the D is changed to the letter C, and the first column now has 1 or 16 decimal places. 16decimal + 12decimal - 15decimal Equals 13decimal, or D in the first column.
Calculating the totals for the next columns does not need any borrowing, thus the process is straightforward. Because one was skipped, C minus A equals 12 decimal minus 10 decimal, which equals 2, and 5 minus 3 also equals 2, so the final answer is 22D.
If the number being subtracted is greater than the number it is being subtracted from, you need only switch the locations of the numbers, do the subtraction, and then add a negative sign to the final result. If the preceding example were written as 3AF - 5DC instead, it would then be written exactly as it is, with the exception that the answer would be -22D.
Multiplication with hexadecimals
Multiplying in hexadecimal might be challenging due to the fact that the conversions between hex and decimal while executing the operations require more work due to the larger numbers that are typically used in hexadecimal. A hexadecimal multiplication table might be quite useful to have on hand (one is provided below).
In that case, performing the conversion from decimal to hexadecimal manually will be required for each step. An illustration of hexadecimal multiplication can be found below. To the right of the example, each of the processes for multiplying and adding are presented in graphical form.
Please take note that all of the numerals used are in the hexadecimal format. If additional information is required, please refer to the following section:
FA3 A = 1E; 1 carried to FC33 F = 2D, and plus 1 = 2E2EEC A = 78; 7 carried to F+BB80C F = B4, and plus 7 = BB = BE6E
Long division in hex is exactly the same as long division in decimal; the only difference is that hexadecimal is used for the multiplication and the subtraction. Converting to decimal allows one to subsequently carry out long division in decimal, after which the result can be converted back to the original system.
For the sake of clarity, the division example will be worked out entirely in hexadecimal notation. When performing hex division, possessing a hexadecimal multiplication table (an example of which is shown below) is helpful in the same way as it is when performing hex multiplication.
The example is below below. Take note that all of the numerals in the example are in the hexadecimal format. Although borrowing does not take place in the example that follows, it is important to keep in mind that borrowing in hex results in the borrowing of 16 decimal rather than 10 decimal. For further information and clarification, please see the hex subtraction section.
Hexadecimal Table for Multiplication and Division
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