# ⇩ DECIMAL TO BASE N CONVERTERS ⇩

#### DECIMAL TO HEXADECIMAL CONVERTER (WITH STEPS)

Enter a number. RESULT

(100)10 = (64)16 DESCRIPTIONS

Divide the number repeatedly by 16 until the quotient becomes 0.

• When 100 is divided by 16, the quotient is 6 and the remainder is 4.
• When 6 is divided by 16, the quotient is 0 and the remainder is 6.

Write the remainders from bottom to top.

(100)10 = (64)16 OTHER INFORMATION

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# ⇩ DECIMAL TO BASE N CONVERTERS ⇩

## INFORMATION

#### WHOLE NUMBERS

We apply the following rules to convert a decimal number to hexadecimal.

• We divide the decimal number by 16 repeatedly until the quotient becomes 0.
• Starting at the least significant digit, we write the remainders in the same order of divisions. For example, to convert decimal 910 to hexadecimal, we divide 910 by 16 repeatedly until the quotient becomes 0.

When we divide 910 by 16, the quotient is 56 and the remainder is 14. Because 14 is represented by E in base 16, we write E to the least significant digit. We continue the algorithm with 56. When we divide 56 by 16, the quotient is 3 and the remainder is 8. Then 8 is the second least significant digit of the hexadecimal number. Finally, we divide 3 by 16. When we do this operation, the quotient is 0 and the remainder is 3. Because the quotient is 0, we stop the procedure. Then we write the last remainder to the most significant digit. To sum up, the hexadecimal representation of 910 is 38E.

(910)10 = (38E)16

#### DECIMAL NUMBERS

In case, the decimal number is not an integer, we can convert the whole number and fractional parts separately and add the hexadecimal equivalents up.

To convert the fractional part of a decimal number, we apply the following rules.

• We multiply the fractional part by 16 repeatedly until the product becomes an integer or the number of significant digits is sufficient for our calculations.
• At each step, we write the integer part of the rightmost digit to the fractional part of the hexadecimal number. We continue with the fractional part of the product.

For example, to convert decimal 910.69 to hexadecimal, we multiply the fractional part by 16 repeatedly until we find an integer.

• 0.69 × 16 = 11.04
• 0.04 × 16 = 0.64
• 0.64 × 16 = 10.24
• .................. The fractional part of 910.69 is 0.69. When we multiply 0.69 by 16, the result is 11.04. The integer part of 11.64 is 11. Because 11 is equivalent to B in hexadecimal representation, we write B to the first digit on the RHS of the radix point.

0.B

We continue with the fractional part of 11.04. When we multiply 0.04 by 16, the result is 0.64. We write the integer part of 0.64 to the next digit of the hexadecimal number.

0.B0

The fractional part of 0.64 is 0.64. Therefore, we continue with this number. The product of 0.64 and 16 is equal to 10.24. We write the hexadecimal representation of 10 to the next digit.

(0.69)10 = (0.B0A...)16

Hexadecimal representation of 910.69 is equal to the sum of hexadecimal representations of 910 and 0.69. Thus, decimal 910.69 is equal to 38E.B0A... in base 16.

(910.69)10 = (910)10 + (0.69)10

= (38E)16 + (0.B0A...)16

= (38E.B0A...)16

### WHAT IS DECIMAL TO HEXADECIMAL CONVERTER?

• Computes the hexadecimal equivalent of the entered decimal number and
• Describes each step of the conversion for both whole number and fractional parts,

### HOW TO USE DECIMAL TO HEXADECIMAL CONVERTER?

You can use decimal to hexadecimal converter in two ways.

• #### USER INPUTS You can enter a decimal number to the input box and click on the "CONVERT" button. The result and explanations appaer below the calculator

• #### RANDOM INPUTS You can click on the DIE ICON next to the input box. If you use this property, a random decimal number is generated and entered to the calculator, automatically. You can see the result and explanations below the calculator. You can create your own examples and practice using this property.

• #### CLEARING THE INPUT BOX To check the hexadecimal equivalent of other decimals you can clear the input box by clicking on the CLEAR button under the input box.

• You can copy the generated solution by clicking on the "Copy Text" link, appaers under the solution panel.

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