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L5, Hexadecimal System, Conversion of Hexadecimal number into Octal and vice versa, package q10856

Conversion of Hexadecimal number into Octal and vice versa :-

To convert a hex number to an octal, we will first convert the hex number to binary and then to octal.


Below are the detailed steps followed for the above mentioned process:

  1. Convert each hex digit to its corresponding four binary digits (bits) from right to left.
  2. Combine all the binary digits.
  3. Separate the binary digits into groups of 3 bits each from right to left.
  4. Ensure the left most group has 3 bits by prefixing necessary zeros.
  5. Find the octal equivalent of each group and combine the resultant digits together.

For example, hexadecimal number 0x5AF6 is converted into binary as

Hex Number    ->    5    A    F    6
Binary Number ->  0101 1010 1111 0110
Binary Number ->  0101101011110110
Binary Number ->   0 101 101 011 110 110
Binary Number ->  000 101 101 011 110 110 // After prefixing zeros in the left most group
Octal Number  ->   0   5   5   3   6   6
Octal Number  ->   055366

Hence, the octal equivalent of the given hexadecimal number is (55366)8

Similarly an octal can be converted into a hex following the below steps:

  1. Convert each octal digit to its corresponding three binary digits (bits) from right to left.
  2. Combine all the binary digits.
  3. Separate the binary digits into groups of 4 bits each from right to left.
  4. Ensure the left most group has 4 bits by prefixing necessary zeros.
  5. Find the hex equivalent of each group and combine the resultant digits together.

For example, an octal number 0246 is converted into hexadecimal as

Octal Number  ->   2   4   6
Binary Number ->  010 100 110
Binary Number ->  010100110
Binary Number ->     0 1010 0110
Binary Number ->  0000 1010 0110 // After prefixing zeros in the left most group
Hex Number    ->    0    A    6
Hex Number    ->   0X0A6

Hence, the hex equivalent of the given octal number is (A6)16

Select all the correct statements given below.
  • (ABCD)16 is a hexadecimal number.
  • Each hexadecimal digit is represented as four bit binary number.
  • Octal number (157)8 is equivalent to the hexadecimal number (6F)16.
  • Hexadecimal number (369)16 is equivalent of octal number (1561)8.

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