Hexidecimal to Decimal Number Calculator

[ 9 Votes ]

The Hexidecimal to Decimal Number Calculator will calculate:

  1. The corresponding decimal number when its hexadecimal form is known.

Hexidecimal to Decimal Number Calculator Parameters:

Hexidecimal to Decimal Number Calculator
Results (detailed calculations and formula below)
Decimal number =
Hexidecimal to decimal conversion calculations
Hexidecimal to Decimal Number Calculator Input Values
Hexadecimal Number (a) =

Please note that the formula for each calculation along with detailed calculations is shown further below this page. As you enter the specific factors of each hexidecimal to decimal number calculation, the Hexidecimal to Decimal Number Calculator will automatically calculate the results and update the formula elements with each element of the hexidecimal to decimal number calculation. You can then email or print this hexidecimal to decimal number calculation as required for later use.

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[ 9 Votes ]

Theoretical description

In most daily activities we use the decimal system of numerals, which is a system where there only 10 digits are used to express all numbers. They are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Then, these digits are combined to create larger numbers. This combination includes writing numbers as a list of digits, where more in the right a digit be, smaller its value is.

In decimal system of numerals, the value of digits increases 10 times when shifting by one position due left. For example, the rightmost digit of 555 indicates 5 units (or 5 ones), the middle digit indicates 5 tens while the leftmost digit indicates 5 hundreds. In general, for the decimal system of numerals we have

edcba = ⋯ + e × 10,000 + d × 1,000 + c × 100 + b × 10 + a × 1

The three dots mean that the number can be longer and the other possible digits are on the left part.

When expressed in terms of powers of ten (we call this form of numbers representation as "scientific notation"), the above number becomes

edcba = ⋯ + e × 104 + d × 103 + c × 102 + b × 101 + a × 100

If the number is expressed in either of the two forms above, we say the number is decomposed. For example, 70,328 is written in the decomposed form as

70,328 = 7 × 10,000 + 0 × 1,000 + 3 × 100+ 2 × 10 + 8 × 1

or

70,328=7 × 104 + 0 × 103 + 3 × 102 + 2 × 101 + 8 × 100

In addition to the standard binary system of numerals (i.e. the base 2 systems where only 2 digits, 0 and 1 are used to represent numbers) there are other numeric systems. Computer-based systems make use of the hexadecimal system of numerals. It is system of numerals with the base equal to 16 (hexadecimal means "of base 16"), where the value of any digit increases by 16 times when shifting by one position due left. Normally, we have to use 16 different digits to express such numbers (from 0 to 15). From decimal system we have only 10 digits available (from 0 to 9), the rest of digits are expressed by using uppercase letters from A to F. Thus, A = 10, B = 11, C = 12, D = 13, E = 14 and F = 15. The rest of the rules is the same as in the decimal system, i.e. the value of digits increases from right to left, any number can be expressed in the decomposed form, etc. For example, the hexadecimal number 3A9F is expressed in the decomposed form as:

3A9F16 = 3 × 163 + A × 162+9 × 161+F × 160

which corresponds to

3 × 163 + 10 × 162 + 9 × 161 + 15 × 160
= 3 × 4,096 + 10 × 256 + 9 × 16 + 15 × 1
= 12,288 + 2,560 + 144 + 15
= 15,007

in the decimal system of numerals.

We can also convert a number from hexadecimal to decimal by applying recurrent divisions by 16 and eventually consider the remainders of each division from the last to the first. For example, when we want to convert the decimal number 8,439 into hexadecimal, we write

8,439 ÷ 16 = 527 (7)
527 ÷ 16 = 32 (15)
32 ÷ 16 = 2 (0)
2 ÷ 16 = 0 (2)

Thus, since 15 corresponds to the letter 'F' in the hexadecimal system, we obtain

8,439 = 20A716

As you may have noticed, the number base is written as a subscript. Only in the decimal system, it is not necessary to write the base just like the plus before positive numbers.

The calculator presented here will allow you to convert a decimal number to hexadecimal number system in an effortless way. All what you need to do is to insert correctly the values of the decimal number and the calculator will provide its hexadecimal equivalent. This will save you precious time lost during the conversion process through recurrent divisions.

Arithmetic Math Tutorials associated with the Hexidecimal to Decimal Number Calculator

The following Math tutorials are provided within the Arithmetic section of our Free Math Tutorials. Each Arithmetic tutorial includes detailed Arithmetic formula and example of how to calculate and resolve specific Arithmetic questions and problems. At the end of each Arithmetic tutorial you will find Arithmetic revision questions with a hidden answer that reveal when clicked. This allows you to learn about Arithmetic and test your knowledge of Math by answering the revision questions on Arithmetic.