A Binary Number System is composed of two symbols : 0’s (zeroes) and 1’s (ones), which represent low or Off and high or On state respectively in digital electronics. It is primarily a number system with the base-2 and is extensively used in computer science as well. All the data is stored in binary symbols in computers which are also called bits. The Binary System derives its name from the fact that it is composed of just two symbols. A Binary Number can also be thought of as a string of just 0’s and 1’s.
An Octal Number System comprises eight digits ranging from 0 to 7. It derives its name from the fact that it consists of eight digits (hence Oct) which means eight. It is an 8-base number system and can be formulated by grouping the bits in a binary number in groups of three and calculating the corresponding value of each group as a single digit in the resultant Octal Number.
For example Binary to Octal Conversion
Input : 100100 Output: 44 Input : 1100001 Output : 141
Methods for Binary to Octal Conversion
In this article, we are going to explore 2 methods to convert a Binary Number to an Octal Number. These methods are as follows :
- Using the built-in toOctalString() method in Java
- Converting the binary number to a decimal number which is further converted to the corresponding Octal number.
1. Using toOctalString() Method for Binary to Octal Conversion
Using this approach, we first convert a binary number to an Integer and then using the toOctalString() built-in method of Java convert it into a string of octal numbers. This string is then converted to an Integer again.
Syntax of toOctalString
public static String toOctalString(int num)
Parameters: The method accepts a single parameter num of integer type which is required to be converted to a string.
Return Value: The function returns a string representation of the integer argument as an unsigned integer in base 8.
Algorithm:
- Convert the binary number into a decimal number.
- Convert this decimal number to a string of octal numbers using the toOctalString() method.
- Convert this string again to an Integer.
Below is the implementation of the above method:
Java
// Java program to convert binary to octalclass GFG { // method to convert binary to decimal int binaryToDecimal(long binary) { // variable to store the decimal number int decimalNumber = 0, i = 0; // loop to extract the digits of the // binary number while (binary > 0) { // multiplying each digit of binary // with increasing powers of 2 towards // left decimalNumber += Math.pow(2, i++) * (binary % 10); // dividing the binary by 10 // to remove the last digit binary /= 10; } // returning the converted decimal number return decimalNumber; } // function to convert decimal to octal int decimalToOctal(long binary) { // variable to store the decimal number // returned by the binaryToDecimal() int decimalNumber = binaryToDecimal(binary); // using the toOctalString() to convert // Integer to String of Octal Number String octalString = Integer.toOctalString(decimalNumber); // converting the String of octal number // to an Integer int octalNumber = Integer.parseInt(octalString); // returning the octal number return octalNumber; } // Driver Code public static void main(String[] args) { // instantiating the class GFG ob = new GFG(); // calling and printing the decimalToOCtal // method System.out.println("octal number:" + ob.decimalToOctal(100100)); }} |
octal number:44
2. User Defined Function to Convert Binary to Octal
Using this approach, we first convert the binary number to a decimal number. We then convert this decimal number to an octal number by continuously extracting the remainder and dividing by 8.
Algorithm:
- Convert the binary number to a decimal number.
- Now, for this converted decimal number, run a while loop till this number becomes 0.
- In every iteration of the loop, get the remainder by dividing the number by 8.
- Multiply this remainder with increasing powers of 10.
- Finally divide the original number by 8.
Example:
Java
// Java program to convert binary to octal// Driver Classclass GFG { // function to convert binary number // to decimal number int binaryToDecimal(long binary) { // variable to store the converted // decimal number int decimalNumber = 0, i = 0; // loop to convert binary to decimal while (binary > 0) { // extracting every digit of the // binary and multiplying with // increasing powers of 2 decimalNumber += Math.pow(2, i++) * (binary % 10); // dividing the number by 10 // to remove the last digit binary /= 10; } // returning the converted decimal // number return decimalNumber; } // function to convert decimal number // to octal int decimalToOctal(long binary) { // variable to store the octal number int octalNumber = 0, i = 0; // variable to store the output // returned by the binaryToDecimal() int decimalNumber = binaryToDecimal(binary); // loop to convert decimal to octal while (decimalNumber != 0) { // extracting the remainder on // multiplying by 8 and // dividing that with increasing // powers of 10 octalNumber += (decimalNumber % 8) * ((int)Math.pow(10, i++)); // removing the last digit by // dividing by 8 decimalNumber /= 8; } // returning the converted octal number return octalNumber; } // Driver Code public static void main(String[] args) { // instantiating the class GFG ob = new GFG(); // calling and printing the // decimalToOctal() function System.out.println(ob.decimalToOctal(1001001)); }} |
111
The complexity of the above method:
Time complexity: O(nlogn) as using pow function inside while loop
Auxiliary space: O(1)
