Decimal to Hex Conversion: Table, Conversion

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Decimal to Hex conversion can be better understood by first knowing about decimal and hexadecimal number systems.

The base of a decimal number system is 10, often known as a radix.
Therefore, it has 10 symbols, i.e. the digits 0 to 9, indicated as 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
The base or radix of a hexadecimal number system is 16.
As a base-16 numeric system, it uses 16 symbols.
These contain the 10 decimal numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), as well as the first 6 letters of the English alphabet (A, B, C, D, E, and F).
However, these letters are used to represent the numbers 10, 11, 12, 13, 14, and 15 in a single figure.

Table of Content

What is the Decimal Number System?
What is the Hexadecimal Number System?
Convert Decimal to Hexadecimal
Decimal to Hexadecimal Table
Decimal to Hexadecimal Conversion With Steps
Solved Examples
Things to Remember
Sample Questions

Key Terms: Decimal, Hexadecimal, Number system, Face value, Place value, Base 10, Base 16, Radix, Digits, Integers, Division, Quotient, Remainder

What is the Decimal Number System?

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The decimal number system is the oldest number system that has its base as 10 which includes 0-9 digits.

Its base is also known as the radix.
All the numbers in any number system contain two basic terms which are face value and place value.
The face value is the number itself and the place value is the magnitude of the position of the number given.
For example, consider a number 7654, in this, the face value of 6 is 6 itself whereas the place value is 600.

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What is the Hexadecimal Number system?

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The hexadecimal number system is the system in which the base value is 16 which includes 0-9 digits, i.e. 0.,1, 2, 3, 4, 5, 6, 7, 8, 9, and A to F alphabets, i.e. A, B, C, D, E, and F.

The alphabet can also be represented using the numbers such as 10,11,12,13,14,15.
The hexadecimal number system is also called the base 16 number system as its radix is 16.

Convert Decimal to Hexadecimal

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The conversion of decimal numbers to hexadecimal numbers is fairly easy. It is possible to carry out this using a conversion table. Using this table, we can convert a decimal number to a hexadecimal number easily.

Each decimal number from 1 to 15 has a corresponding hexadecimal number.
But to convert a decimal value that is more than 15 we need to follow a different procedure.
If a given number is more than 15, we must divide it by 16 and take the remainder to obtain the corresponding hexadecimal number.

Decimal to Hex Conversion

Decimal to Hexadecimal Table

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To convert the decimal number system to hex, students must know the table below in order to answer problems easily.

Decimal Number	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
Equivalent Hexadecimal	0	1	2	3	4	5	6	7	8	9	A	B	C	D	E	F

Decimal to Hexadecimal Conversion With Steps

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Follow the steps given below to learn how to convert numbers from decimal to hex.

Step 1: First, divide the decimal number by 16, considering it as an integer.
Step 2: Keep aside the remainder.
Step 3: Divide the quotient again by 16 and repeat until the quotient value equals zero.
Step 4: To obtain the hexadecimal numbers, reverse the values of the remainder left.

Remember that integers from 0 to 9 are counted the same in the decimal system. However, from 10 to 15, they are expressed in alphabetical sequence as A, B, C, D, E, F, and so on.

Example of Decimal to Hexadecimal Conversion

Example: Convert (830)₁₀ into hexadecimal.

Ans. The following step should be taken to convert 830 base 10 to a hexadecimal number

Step 1: First divide 830 by 16.
830 ÷ 16 = 51 and remainder = 14

Step 2: Again, divide the quotient 51 by 16.
51 ÷ 16 = 3 and the remainder = 3.

Step 3: Again dividing 3 by 16, will leave quotient = 0 and remainder = 3.

Step 4: Taking the remainder in reverse order and substituting the right hexadecimal value for them, we get,
3 → 3

3 → 3

14 → E

Therefore, (830)₁₀ = (33E)₁₆

Solved Examples

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Ques. Convert 60₁₀ into a hexadecimal number.

Ans. The given decimal number is 60₁₀

Divide by 16	Quotient	Remainder	Hex Value
60 ÷ 16	3	12	C
3 ÷ 16	0	3	3

Therefore, 60₁₀ = 3C₁₆

Ques. Convert 487₁₀ into a hexadecimal number.

Ans. The given decimal number is 487₁₀

Divide by 16	Quotient	Remainder	Hex Value
487/16	30	7	7
30/16	1	14	E
1/16	0	1	1

Therefore, 487₁₀ = 1E7₁₆

Ques. Convert 1234₁₀ into a hexadecimal number.

Ans. The given decimal number is 1234₁₀

Divide by 16	Quotient	Remainder	Hex Value
1234/16	77	2	2
77/16	4	13	D
4/16	0	4	4

Therefore, 1234₁₀ = 4D2₁₆

Things to Remember

The decimal number system has a base or the radix as 10.
The base contains the numbers 0-9 which are 0,1,2,3,4,5,6,7,8,9.
The hexadecimal number system has a base or the radix as 16.
The radix of the hexadecimal number contains the numbers 0-9 and the letters of alphabets A-F.
The letters are taken in the place of 10,11,12,13,14,15.
The conversion of decimal to hexadecimal is done by dividing the given decimal number by 16 until we get a number less than 16.
The process continues by multiplying all the obtained remainder by 16.

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Sample Questions

Ques. What is the decimal number system? Discuss. (2 Marks)

Ans. The decimal number system is the earliest known number system. It has its base which is also known as the radix as 10. The radix includes the digits from 0-9 which are 0,1,2,3,4,5,6,7,8,9. The decimal number system can easily be converted to any other number system with the help of their respective tables.

Ques. What do you mean by the hexadecimal number system? Discuss. (2 Marks)

Ans. The hexadecimal number system is one of the number systems that has its base or the radix as 16. The radix of the hexadecimal number system contains digits from 0-9 and also the English alphabets from A-F. These alphabets represent the numbers 10-15.

Ques. In the conversion of decimal to hex, what is the change in their bases? (1 Mark)

Ans. When converting decimal to hex, base 10 numbers are converted to base 16 numbers.

Ques. What is the hex equivalent to the decimal number 13? (1 Mark)

Ans. The hex equivalent to the decimal number 13 is D.

Ques. Discuss the steps to convert decimal to hexadecimal numbers. (3 Marks)

Ans. The decimal number system can be converted to the hexadecimal number in the following steps:

Divide the taken decimal number by 16.
If the number is greater than 16, continue the process.
As soon as you get a number less than 16, take it as the first decimal digit.
Multiply the previously obtained decimal remainders by 16.
Write all the pre-decimal digits and convert them into the hexadecimal number system using its radix.

Ques. Convert 7637₁₀ into a hexadecimal system. (3 Marks)

Ans. The given number is 7637.

Firstly, divide the given number by 16 and the remainder until we get a number less than 16.

7637/16 = 477.3125

477.3125/16 = 29.8320

29.8320/16 = 1.8645

So 1 is less than 16. The first decimal number is 1.

Now, multiply the post-decimal digits by 16.

0.8645×16 = 13.832

0.8320×16 = 13.312

0.3125×16 = 5

So, the number is 1-13-13-5.

The hexadecimal equivalent is 1DD5.

Ques. What would be the hexadecimal equivalent for 525₁₀? (3 Marks)

Ans. Given number: 525

Divide the given number by 16 until we get a number less than 16.

525/16 = 32.8125

32.8125/16 = 2.050.

The first decimal number is 2

Multiply the reminders by 16.

0.050×16 = 0.8

0.8125×16 = 13

So the number is 2-0-13 and the hexadecimal equivalent is 20D.

Ques. Convert 667₁₀to its hexadecimal equivalent In tabular form. (3 Marks)

Ans.

Divide by 16 Quotient Remainder Hexadecimal equivalent

Divide by 16	Quotient	Remainder	Hex Value
667 ÷ 16	41	11	B
41 ÷ 16	2	9	9
2 ÷ 16	0	2	2

Hence, the hexadecimal equivalent is 29B₁₆.

Ques. Convert 8740₁₀ to its hexadecimal equivalent In tabular form. (3 Marks)

Ans.

Divide by 16	Quotient	Remainder	Hex Value
8740 ÷ 16	546	4	4
546 ÷ 16	34	2	2
34 ÷ 16	2	2	2
2 ÷ 16	0	2	2

Hence, the hexadecimal equivalent is 2224₁₆.

Ques. Convert 27338₁₀ into a hexadecimal number. (4 Marks)

Ans. Given number: 27338

Step 1: Divide 27338 by 16.

27338/16 = 1708.6250

Step 2: Repeat the process till you get a number less than 16.

1708.6250/16 = 106.7890

106.7890/16 = 6.6743

Step 3: Consider the first digit as the decimal number.

Step 4: Multiply the previously obtained post-decimal remainders by 16.

0.6743×16 = 10.788

0.7890×16 = 12.624

0.6250×16 = 10

Hence the number is 6-10-12-10.

In the hexadecimal system, the number is 6ACA.

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Decimal to Hex Conversion: Table, Conversion

What is the Decimal Number System?

What is the Hexadecimal Number system?

Convert Decimal to Hexadecimal

Decimal to Hexadecimal Table

Decimal to Hexadecimal Conversion With Steps

Example of Decimal to Hexadecimal Conversion

Solved Examples

Things to Remember

Sample Questions

CBSE CLASS XII Related Questions

1.
A carpenter needs to design a wooden box in the shape of a cuboid such that the sum of its length and breadth is 3 cm more than its height. Twice of its length, thrice of its breadth and its height add up to 10 cm. Its breadth added to 7 times its height is 1 cm less than 3 times its length.

2.
Find:

If the function \[ f(x)= \begin{cases} \frac{\sin x}{x}+\cos x, & x\neq0\\ k, & x=0 \end{cases} \] is continuous at \(x=0\), then find the value of \(k\).

3.
Find:
Let \(A=[a_{ij}]\) be a \(2\times2\) matrix whose elements are given by \[ a_{ij}=\frac{(2i-j)^2}{3} \] Find the transpose matrix \(A'\).

4.
At a birthday party, children are being served orange juice in conical cups, as shown in the figure.

Each cup is 15 cm deep and has a radius 5 cm. The juice is being poured into this cup at a rate of 0·1 cm3/s.
On the basis of the above information, answer the following questions :

6.
Using integration, find the area of the region bounded by the curve \( y = x|x| \), the x-axis, and the vertical lines \( x = -2 \) and \( x = 2 \).

Comments

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Decimal to Hex Conversion: Table, Conversion

What is the Decimal Number System?

What is the Hexadecimal Number system?

Convert Decimal to Hexadecimal

Decimal to Hexadecimal Table

Decimal to Hexadecimal Conversion With Steps

Example of Decimal to Hexadecimal Conversion

Solved Examples

Things to Remember

Sample Questions

CBSE CLASS XII Related Questions

1.A carpenter needs to design a wooden box in the shape of a cuboid such that the sum of its length and breadth is 3 cm more than its height. Twice of its length, thrice of its breadth and its height add up to 10 cm. Its breadth added to 7 times its height is 1 cm less than 3 times its length.

2. Find: If the function \[ f(x)= \begin{cases} \frac{\sin x}{x}+\cos x, & x\neq0\\ k, & x=0 \end{cases} \] is continuous at \(x=0\), then find the value of \(k\).

3.Find:Let \(A=[a_{ij}]\) be a \(2\times2\) matrix whose elements are given by \[ a_{ij}=\frac{(2i-j)^2}{3} \] Find the transpose matrix \(A'\).

4.At a birthday party, children are being served orange juice in conical cups, as shown in the figure. Each cup is 15 cm deep and has a radius 5 cm. The juice is being poured into this cup at a rate of 0·1 cm3/s.On the basis of the above information, answer the following questions :

6.Using integration, find the area of the region bounded by the curve \( y = x|x| \), the x-axis, and the vertical lines \( x = -2 \) and \( x = 2 \).

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
A carpenter needs to design a wooden box in the shape of a cuboid such that the sum of its length and breadth is 3 cm more than its height. Twice of its length, thrice of its breadth and its height add up to 10 cm. Its breadth added to 7 times its height is 1 cm less than 3 times its length.

2.
Find:

If the function \[ f(x)= \begin{cases} \frac{\sin x}{x}+\cos x, & x\neq0\\ k, & x=0 \end{cases} \] is continuous at \(x=0\), then find the value of \(k\).

3.
Find:
Let \(A=[a_{ij}]\) be a \(2\times2\) matrix whose elements are given by \[ a_{ij}=\frac{(2i-j)^2}{3} \] Find the transpose matrix \(A'\).

4.
At a birthday party, children are being served orange juice in conical cups, as shown in the figure.

Each cup is 15 cm deep and has a radius 5 cm. The juice is being poured into this cup at a rate of 0·1 cm3/s.
On the basis of the above information, answer the following questions :

6.
Using integration, find the area of the region bounded by the curve \( y = x|x| \), the x-axis, and the vertical lines \( x = -2 \) and \( x = 2 \).