Hexadecimal to octal conversion involves first converting the hexadecimal number into binary, and then converting that binary number into octal. Here's how to do it:
Steps to Convert Hexadecimal to Octal:
Convert the hexadecimal number to binary.
Each hexadecimal digit corresponds to a 4-bit binary equivalent.
Group the binary number into sets of 3 bits starting from the right. If necessary, add leading zeros to the leftmost group to make it a full group of 3 bits.
Convert each 3-bit group into its octal equivalent.
Binary 000 = Octal 0
Binary 001 = Octal 1
Binary 010 = Octal 2
Binary 011 = Octal 3
Binary 100 = Octal 4
Binary 101 = Octal 5
Binary 110 = Octal 6
Binary 111 = Octal 7
Write down the octal digits corresponding to each 3-bit group.
Example:
Convert hexadecimal 1A3 to octal:
Convert hexadecimal to binary:
1 = 0001
A = 1010
3 = 0011
So, hexadecimal 1A3 becomes binary 0001 1010 0011.
Group the binary number into sets of 3 bits:
000
110
100
011
000 110 100 011
Add leading zeros if necessary to make complete sets of 3 bits:
000
001
101
000
011
000 001 101 000 011
Convert each 3-bit group to octal:
000 = 0
001 = 1
101 = 5
000 = 0
011 = 3
Write the octal number:
1
𝐴
3
(hex)
=
0153
(octal)
1A3 (hex)=0153 (octal)
So, 1A3 in hexadecimal is 153 in octal.