Octal to Hexadecimal Conversion: Definition, Table & Solved Examples
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There are four different number system conventions: hexadecimal, octal, decimal, and binary. Compared to the lengthy binary strings of 1s and 0s, the "Hexadecimal" or "Hex" numbering system, which employs the Base of 16 system, is a common choice for encoding large binary values. For computer languages to interpret huge binary numbers, the octal and hexadecimal number systems have been developed. Base-8 is used in the octal number system, while base-16 is used in the hexadecimal number system. designers and programmers of computer systems most frequently use hexadecimal numbers.
In this Maths article we will look Octal to Hexadecimal definition, conversion, table, and solved examples in detail.
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Octal Number System
A base 8 number system is referred to as an octal number system. As a result, there are a total of eight different symbols that can be used to represent numbers: 0, 1, 2, 3, 4, 5, 6, and 7.
For example, under an octal number system, the number 8 would be written as 8, the number 9 as 9, and so on.
The octal number system was employed in these systems because it offered a more user-friendly method of representing numbers than the binary number system.
Hexadecimal Number System
One method of representing numbers that has a base value of 16 is the hexadecimal number system.
The numerical value of each digit in the hexadecimal sequence is obtained by multiplying the number by the power of 16, which depends on the position of the number, and then adding the result to the sum. This means that in a hexadecimal system of numbers, each digit is 16 times more valuable than the previous digit.
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What is Octal to Hexadecimal Conversion?
It is common practice to convert from octal to hexadecimal by first turning the octal number into a binary digit, and then from binary to hexadecimal.
For example: 536 from octal to hexadecimal conversion
Solution:
When we convert 536 (octal) into binary, we get
(536)₈ = (101) (011) (110)
= (101011110)₂
To get its hexadecimal equivalent, we now group the four binary bits together.
(101011110)₂ = (0001)(0101)(1110)
= (15E)₁₆
536 is represented by the hexadecimal value 15E.
How to convert octal to hexadecimal
Two steps are required to change an octal number to hexadecimal.
Step : 1 We first convert the octal number into binary.
46.1
In order to convert an octal number to binary, we must write each octal digit's 3 bit binary equivalent in the same order.
(46.1)₈ = (100110.001)₂
The binary number is changed to hexadecimal in the following step.
0010110.0010
The binary number divides into groups of four bits starting at the binary point. When dealing with whole numbers, we move to the left, and when dealing with fractions, we move to the right.
(10011.001)₂ = (26.2)₁₆
The following outcome is reached by using the equalities that we discovered in steps 1 and 2.
(46.1)₈ = (26.2)₁₆
Octal to Hexadecimal Conversion Table
The Octal to Hexadecimal Conversion Table helps convert numbers from base-8 (octal) to base-16 (hexadecimal). To convert, first change the octal number to binary, then group the binary digits into 4s, and convert to hexadecimal. This table makes conversion quick and easy.
|
Octal number |
Hexadecimal number |
|
0 |
0 |
|
1 |
1 |
|
2 |
2 |
|
3 |
3 |
|
4 |
4 |
|
5 |
5 |
|
6 |
6 |
|
7 |
7 |
|
10 |
8 |
|
11 |
9 |
|
12 |
a |
|
13 |
b |
|
14 |
c |
|
15 |
d |
|
16 |
e |
|
17 |
f |
|
20 |
10 |
Hex to Octal Conversion Table
|
Hexadecimal |
Octal |
Decimal |
Binary |
|
0 |
0 |
0 |
0000 |
|
1 |
1 |
1 |
0001 |
|
2 |
2 |
2 |
0010 |
|
3 |
3 |
3 |
0011 |
|
4 |
4 |
4 |
0100 |
|
5 |
5 |
5 |
0101 |
|
6 |
6 |
6 |
0110 |
|
7 |
7 |
7 |
0111 |
|
8 |
10 |
8 |
1000 |
|
9 |
11 |
9 |
1001 |
|
A |
12 |
10 |
1010 |
|
B |
13 |
11 |
1011 |
|
C |
14 |
12 |
1100 |
|
D |
15 |
13 |
1101 |
|
E |
16 |
14 |
1110 |
|
F |
17 |
15 |
1111 |
Solved Examples of Octal to Hexadecimal
Problem: 1
What is the hexadecimal equivalent of (50)₈?
Solution:
Octal is first converted to binary before being converted to hexadecimal. Looking at the table of the octal to binary conversion,
5 = 101
0 = 000
(50)₈ = (101000)₂
As we can see from the binary to hexadecimal conversion table,
0010 = 2
1000 = 8
As the result, the hexadecimal equivalent of (50)₈ = (28)₁₆
Problem : 2
Covert the octal number (56)₈ to a hexadecimal number.
Solution:
First convert (56)₈ into binary number
(56)₈
= (101)(110)
= (101110)₂
Now convert (101110)₂ in hexadecimal
(101110)₂
= (10)(1110)
= (2)(14)
= (2E)₁₆
Problem : 3
Covert the octal (36.125)₈ to Decimal Conversion
Solution:
= 3 × 8¹ + 6 × 8⁰ + 1 × 8⁻¹ + 2 × 8⁻² + 5 × 8⁻³
= 24 + 6 + 0.125 + 0.03125 + 0.009765625
= (30.16601563)₁₀
Decimal number = (30.16601563)₁₀
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FAQ For Octal to Hexadecimal
What is Octal to Hexadecimal Conversion?
The simplest method is to change an octal number to a decimal, and then a decimal to hexadecimal form.
What is the Octal Number System?
The term "octal number system" refers to a system of numbers using "eight" as its fundamental unit.
What is a Hexadecimal Number System?
The numerical system with base 16 is known as hexadecimal.
What is the relationship between octal and hexadecimal?
The bases of the hexadecimal, octal, and decimal systems are 16, 8, and 10 respectively. Four binary digits are paired in hexadecimal. Three binary digits are coupled in the octal system.
What are the rules to convert octal to hexadecimal?
Any octal number can be converted to the hexadecimal system by first converting it to binary, and then from binary to hexadecimal.
Is there a direct method to convert octal to hexadecimal?
A: While direct conversion is possible, it’s less common and more complex. Converting via binary is simpler and less error-prone.
Can fractional octal numbers be converted to hexadecimal?
Yes. Convert the integer and fractional parts separately by converting each octal digit to binary, then regrouping and converting to hexadecimal.
Can I convert directly from octal to hexadecimal?
Not directly. You must go through binary as an intermediate step for accurate conversion.
What is the use of the conversion table?
The table provides a quick reference to match octal values to their hexadecimal counterparts, saving time during manual conversions.
Are octal and hexadecimal used in real life?
Yes, they are used in computer programming, digital electronics, and low-level hardware design for easier representation of binary data.