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Hexadecimal numerals are those with a base of 16 characters. Thus, 16 distinct digits represent the numbers. It's abbreviated as h16, with h denoting a hexadecimal number. It could be a mixture of letters and digits. As a result, it includes the digits 0 - 9 and the letters A - F.
Example: (9B)16, (D5)16, (ABC)16
The base of octal numbers is 8. These numbers have digits ranging from 0 - 7 for a maximum of eight digits and are referred to as the octal number system. The base of octal numbers is 8. It's written as o8, with o being an octal number. It does not represent a number with the digits 8 and 9.
Example: (233)8, (115)8, (75)8
To begin, we must translate hexadecimal to its decimal counterpart, then decimal to octal. Follow the steps given below:
Another method for converting any hexadecimal to its octal counterpart exists. We know that hexadecimal numbers contain binary digits, so we can group them into a pair and compare them to octal numbers. Let's take a look at the method with several examples and steps:
Let us see an example here:
Example: Convert ACB into an octal number.
Solution: Given, ACB is a hexadecimal number.
A → 1010, C →1100, B → 1011
Next, arrange them from right to left, each with three digits.
101, 011, 001, 011
101→5, 011 →3, 001→1, 011→3
Hence, ACB = 5313
Hexadecimal | Octal | Equivalent Decimal | Equivalent Binary |
0 | 0 | 0 | 0 |
1 | 1 | 1 | 1 |
2 | 2 | 2 | 10 |
3 | 3 | 3 | 11 |
4 | 4 | 4 | 100 |
5 | 5 | 5 | 101 |
6 | 6 | 6 | 110 |
7 | 7 | 7 | 111 |
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 |
Example: Find the equivalent octal form of 56E.
Solution:
Given, a hexadecimal number is 56E
E = 14 (in decimal)
56E = (5 × 162) + (6 × 161) + (14 x 160)
= (5 x 256) + (6 x 16) + (14 x 1)
=1280 + 96 + 14 = 1390
56E =1390 (Decimal form)
Now we have to convert this decimal to octal number;
The octal number is 2556
Hence, 56E = 2556