# Program to Convert Hexadecimal to Octal

Given a Hexadecimal number, the task is to convert it into an Octal number.

Examples:

```Input: Hexadecimal = 1AC
Output: Binary = 0654
Explanation:
Equivalent binary value of 1: 0001
Equivalent binary value of A: 1010
Equivalent binary value of C: 1100

Grouping in terms of 3: 000 110 101 100

Equivalent octal value of 000: 0
Equivalent octal value of 110: 6
Equivalent octal value of 101: 5
Equivalent octal value of 100: 4

Input: Hexadecimal = 5D1F
Output: Octal = 56437
```

Approach:
A hexadecimal number is a positional numeral system with a radix, or base, of 16 and uses sixteen distinct symbols.

An octal number or oct for short is the base-8 number and uses the digits 0 to 7. Octal numerals can be made from binary numerals by grouping consecutive binary digits into groups of three (starting from the right).

Steps of Conversion

1. Find the equivalent binary number for each digit of the given hexadecimal number. Add 0’s to the left if any of the binary equivalent is shorter than 4 bits.
2. Separate the binary digits into groups, each containing 3 bits or digits from right to left. Add 0s to the left, if the last group contains less than 3 bits.
3. Find the octal equivalent for each binary group.

Below is the implementation of the above approach:

## C

 `// C program to convert ` `// Hexadecimal to Octal ` ` `  `#include ` `#include ` `#include ` ` `  `// Function to convert HexaDecimal to Binary ` `long` `long` `int` `hex_to_bin(``char` `hex[]) ` `{ ` `    ``long` `long` `int` `bin, place; ` `    ``int` `i = 0, rem, val; ` ` `  `    ``bin = 0ll; ` `    ``place = 0ll; ` ` `  `    ``// Hexadecimal to binary conversion ` `    ``for` `(i = 0; hex[i] != ``'\0'``; i++) { ` `        ``bin = bin * place; ` ` `  `        ``switch` `(hex[i]) { ` `        ``case` `'0'``: ` `            ``bin += 0; ` `            ``break``; ` `        ``case` `'1'``: ` `            ``bin += 1; ` `            ``break``; ` `        ``case` `'2'``: ` `            ``bin += 10; ` `            ``break``; ` `        ``case` `'3'``: ` `            ``bin += 11; ` `            ``break``; ` `        ``case` `'4'``: ` `            ``bin += 100; ` `            ``break``; ` `        ``case` `'5'``: ` `            ``bin += 101; ` `            ``break``; ` `        ``case` `'6'``: ` `            ``bin += 110; ` `            ``break``; ` `        ``case` `'7'``: ` `            ``bin += 111; ` `            ``break``; ` `        ``case` `'8'``: ` `            ``bin += 1000; ` `            ``break``; ` `        ``case` `'9'``: ` `            ``bin += 1001; ` `            ``break``; ` `        ``case` `'a'``: ` `        ``case` `'A'``: ` `            ``bin += 1010; ` `            ``break``; ` `        ``case` `'b'``: ` `        ``case` `'B'``: ` `            ``bin += 1011; ` `            ``break``; ` `        ``case` `'c'``: ` `        ``case` `'C'``: ` `            ``bin += 1100; ` `            ``break``; ` `        ``case` `'d'``: ` `        ``case` `'D'``: ` `            ``bin += 1101; ` `            ``break``; ` `        ``case` `'e'``: ` `        ``case` `'E'``: ` `            ``bin += 1110; ` `            ``break``; ` `        ``case` `'f'``: ` `        ``case` `'F'``: ` `            ``bin += 1111; ` `            ``break``; ` `        ``default``: ` `            ``printf``(``"Invalid hexadecimal input."``); ` `        ``} ` ` `  `        ``place = 10000; ` `    ``} ` ` `  `    ``return` `bin; ` `} ` ` `  `// Function to convert Binary to Octal ` `long` `long` `int` `bin_to_oct(``long` `long` `bin) ` `{ ` `    ``long` `long` `int` `octal, place; ` `    ``int` `i = 0, rem, val; ` ` `  `    ``octal = 0ll; ` `    ``place = 0ll; ` ` `  `    ``place = 1; ` ` `  `    ``// Binary to octal conversion ` `    ``while` `(bin > 0) { ` `        ``rem = bin % 1000; ` ` `  `        ``switch` `(rem) { ` `        ``case` `0: ` `            ``val = 0; ` `            ``break``; ` `        ``case` `1: ` `            ``val = 1; ` `            ``break``; ` `        ``case` `10: ` `            ``val = 2; ` `            ``break``; ` `        ``case` `11: ` `            ``val = 3; ` `            ``break``; ` `        ``case` `100: ` `            ``val = 4; ` `            ``break``; ` `        ``case` `101: ` `            ``val = 5; ` `            ``break``; ` `        ``case` `110: ` `            ``val = 6; ` `            ``break``; ` `        ``case` `111: ` `            ``val = 7; ` `            ``break``; ` `        ``} ` ` `  `        ``octal = (val * place) + octal; ` `        ``bin /= 1000; ` ` `  `        ``place *= 10; ` `    ``} ` ` `  `    ``return` `octal; ` `} ` ` `  `// Function to Convert ` `// Hexadecimal Number to Octal Number ` `long` `long` `int` `hex_to_oct(``char` `hex[]) ` `{ ` `    ``long` `long` `int` `octal, bin; ` ` `  `    ``// convert HexaDecimal to Binary ` `    ``bin = hex_to_bin(hex); ` ` `  `    ``// convert Binary to Octal ` `    ``octal = bin_to_oct(bin); ` ` `  `    ``return` `octal; ` `} ` ` `  `// driver code ` `int` `main() ` `{ ` ` `  `// Get the hexadecimal number ` `    ``char` `hex[20] = ``"1AC"``; ` ` `  `// convert hexadecimal to octal ` `    ``printf``(``"Equivalent Octal Value = %lld"``, ` ` ``hex_to_oct(hex)); ` ` `  `    ``return` `0; ` `} `

My Personal Notes arrow_drop_up

Article Tags :
Practice Tags :

Be the First to upvote.

Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.