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Hexadecimal to Octal Conversion

Hexadecimal to Octal Conversion

 

Hexadecimal numbers

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

Octal numbers

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

Hexadecimal to Octal Conversion (Method 1)

To begin, we must translate hexadecimal to its decimal counterpart, then decimal to octal. Follow the steps given below:

  • Take the given hexadecimal number
  • Count the number of digits in the given number
  • Multiply each digit by 16^(n-1) if n is the position of the digit from the right end
  • After you've multiplied the terms, add them together.
  • The obtained number is in the decimal number system.
  • Divide the decimal number with 8
  • Make a list of the remaining items.
  • With the quotient, repeat the previous two steps until the quotient is zero.
  • Reverse the order of the remainders.
  • The obtained number corresponds to the desired outcome.

Hexadecimal to Octal Conversion (Method 2)

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:

  • Write the equivalent binary integer for each hexadecimal number digit. Add 0s to the left side of any binary equivalents that are fewer than 4 digits.
  • From right to left, combine and create groups of binary digits, each containing three digits. If the last group has less than three numbers, add 0's to the left.
  • Find each binary group's octal equivalent.

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 number to Octal number Conversion Table

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;

image

The octal number is 2556
Hence, 56E = 2556

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