Skip to content

How to Convert Hexadecimal to Octal

Published: at 05:30 AM

Converting hexadecimal to octal is a common task in computer programming. Hexadecimal is a base-16 number system that uses sixteen digits, 0 through 9 and A through F. Octal, on the other hand, is a base-8 number system that uses eight digits, 0 through 7. Converting hexadecimal to octal involves converting the hexadecimal number to binary, and then converting the binary number to octal.

Conversion

Here’s a step-by-step guide on how to convert hexadecimal to octal:

  1. Choose the hexadecimal number you want to convert to octal.
  2. Convert the hexadecimal number to binary using the table below.
  3. Group the binary digits into groups of three, starting from the rightmost digit. If the leftmost group has less than three digits, add leading zeros to make it a group of three.
  4. Convert each group of three binary digits to its octal equivalent using the table below.
  5. Write the octal equivalent of each group of three binary digits in order to get the octal representation of the binary number.

Example

Let’s walk through an example to illustrate the process. Suppose we want to convert the hexadecimal number 2A to octal.

  1. The hexadecimal number we want to convert is 2A.
  2. We convert the hexadecimal number to binary using the table below: 0010 1010.
  3. We group the binary digits into groups of three: 000 101 010.
  4. We convert each group of three binary digits to its octal equivalent using the table below. 000 = 0, 101 = 5, 010 = 2.
  5. We write the octal equivalent of each group of three binary digits in order to get the octal representation of the binary number: 052.

Hexadecimal-Binary Table

HexadecimalBinary
00000
10001
20010
30011
40100
50101
60110
70111
81000
91001
A1010
B1011
C1100
D1101
E1110
F1111

Binary-Octal Table

BinaryOctal
0000
0011
0102
0113
1004
1015
1106
1117

References