A number system can be considered as a mathematical notation of numbers using a set of digits or symbols. In simpler words, the number system is a method of representing numbers. Every number system is identified with the help of its base or radix.
For example, Binary, Octal, Decimal and Hexadecimal Number systems are used in microprocessor programming. In this article, one such number system is discussed.
Ternary Number System:
If the Base value of a number system is 3, then this representation is known as a ternary representation. The digits in this system are 0, 1, and 2.
There is also a number system called Balanced Ternary which comprises the digits −1, 0 and +1. The Ternary representation of a number is compact than of binary number system.
Steps to Convert Decimal to Ternary:
- Divide the number by 3.
- Get the integer quotient for the next iteration.
- Get the remainder for the ternary digit.
- Repeat the steps until the quotient is equal to 0.
For example: let N = 101. The following image illustrates the step by step conversion of 10110 to the base-3.
Below is the implementation for the Decimal to Binary and Vice-Versa:
// C++ program to convert decimal // number to ternary number #include <cstdio> #include <iostream> #include <math.h> using namespace std;
// Function to convert a decimal // number to a ternary number void convertToTernary( int N)
{ // Base case
if (N == 0)
return ;
// Finding the remainder
// when N is divided by 3
int x = N % 3;
N /= 3;
if (x < 0)
N += 1;
// Recursive function to
// call the function for
// the integer division
// of the value N/3
convertToTernary(N);
// Handling the negative cases
if (x < 0)
cout << x + (3 * -1);
else
cout << x;
} // Function to convert the decimal to ternary void convert( int Decimal)
{ cout << "Ternary number of "
<< Decimal << " is: " ;
// If the number is greater
// than 0, compute the
// ternary representation
// of the number
if (Decimal != 0) {
convertToTernary(Decimal);
}
else
cout << "0" << endl;
} // Driver code int main()
{ int Decimal = 2747;
convert(Decimal);
return 0;
} |
// Java program to convert decimal // number to ternary number import java.io.*;
class GFG
{ // Function to convert a decimal // number to a ternary number static void convertToTernary( int N)
{ // Base case
if (N == 0 )
return ;
// Finding the remainder
// when N is divided by 3
int x = N % 3 ;
N /= 3 ;
if (x < 0 )
N += 1 ;
// Recursive function to
// call the function for
// the integer division
// of the value N/3
convertToTernary(N);
// Handling the negative cases
if (x < 0 )
System.out.print( x + ( 3 * - 1 ));
else
System.out.print( x);
} // Function to convert the decimal to ternary static void convert( int Decimal)
{ System.out.print( "Ternary number of " +Decimal + " is: " );
// If the number is greater
// than 0, compute the
// ternary representation
// of the number
if (Decimal != 0 ) {
convertToTernary(Decimal);
}
else
System.out.println( "0" );
} // Driver Code public static void main (String[] args)
{ int Decimal = 2747 ;
convert(Decimal);
} } // This code is contributed by shivanisinghss2110 |
# Python3 program to convert decimal # number to ternary number # Function to convert a decimal # number to a ternary number def convertToTernary(N):
# Base case
if (N = = 0 ):
return ;
# Finding the remainder
# when N is divided by 3
x = N % 3 ;
N / / = 3 ;
if (x < 0 ):
N + = 1 ;
# Recursive function to
# call the function for
# the integer division
# of the value N/3
convertToTernary(N);
# Handling the negative cases
if (x < 0 ):
print (x + ( 3 * - 1 ), end = "");
else :
print (x, end = "");
# Function to convert the # decimal to ternary def convert(Decimal):
print ( "Ternary number of " , Decimal,
" is: " , end = "");
# If the number is greater
# than 0, compute the
# ternary representation
# of the number
if (Decimal ! = 0 ):
convertToTernary(Decimal);
else :
print ( "0" , end = "");
# Driver Code if __name__ = = '__main__' :
Decimal = 2747 ;
convert(Decimal);
# This code is contributed by Rajput-Ji |
// C# program to convert decimal // number to ternary number using System;
class GFG
{ // Function to convert a decimal
// number to a ternary number
static void convertToTernary( int N)
{
// Base case
if (N == 0)
return ;
// Finding the remainder
// when N is divided by 3
int x = N % 3;
N /= 3;
if (x < 0)
N += 1;
// Recursive function to
// call the function for
// the integer division
// of the value N/3
convertToTernary(N);
// Handling the negative cases
if (x < 0)
Console.Write( x + (3 * -1));
else
Console.Write( x);
}
// Function to convert the decimal to ternary
static void convert( int Decimal)
{
Console.Write( "Ternary number of " +Decimal + " is: " );
// If the number is greater
// than 0, compute the
// ternary representation
// of the number
if (Decimal != 0) {
convertToTernary(Decimal);
}
else
Console.WriteLine( "0" );
}
// Driver Code
public static void Main ( string [] args)
{
int Decimal = 2747;
convert(Decimal);
}
} // This code is contributed by AnkitRai01 |
<script> // Javascript program to convert decimal
// number to ternary number
// Function to convert a decimal
// number to a ternary number
function convertToTernary(N)
{
// Base case
if (N == 0)
return ;
// Finding the remainder
// when N is divided by 3
let x = N % 3;
N = parseInt(N / 3, 10);
if (x < 0)
N += 1;
// Recursive function to
// call the function for
// the integer division
// of the value N/3
convertToTernary(N);
// Handling the negative cases
if (x < 0)
document.write(x + (3 * -1));
else
document.write(x);
}
// Function to convert the decimal to ternary
function convert(Decimal)
{
document.write( "Ternary number of " + Decimal + " is: " );
// If the number is greater
// than 0, compute the
// ternary representation
// of the number
if (Decimal != 0) {
convertToTernary(Decimal);
}
else
document.write( "0" + "</br>" );
}
let Decimal = 2747;
convert(Decimal);
// This code is contributed by divyeshrabadiya07. </script> |
Ternary number of 2747 is: 10202202
Time Complexity: O(log3N)
Auxiliary Space: O(log3N)
Steps to Convert Ternary to Decimal:
- Connect each digit from the ternary number with its corresponding power of three.
- Multiply each digit with its corresponding power of three and Add up all of the numbers you got.
For example: let N = 10202. The following image illustrates the step by step conversion of 102023 to the base-10.
Below is the implementation for the Decimal to Binary and Vice-Versa:
// C++ program to convert a // ternary number to decimal number #include <cstdio> #include <iostream> #include <math.h> using namespace std;
// Function to convert a ternary // number to a decimal number void convertToDecimal( int N)
{ cout << "Decimal number of "
<< N << " is: " ;
// If the number is greater than 0,
// compute the decimal
// representation of the number
if (N != 0) {
int decimalNumber = 0,
i = 0, remainder;
// Loop to iterate through
// the number
while (N != 0) {
remainder = N % 10;
N /= 10;
// Computing the decimal digit
decimalNumber += remainder
* pow (3, i);
++i;
}
cout << decimalNumber << endl;
}
else
cout << "0" << endl;
} // Driver code int main()
{ int Ternary = 10202202;
convertToDecimal(Ternary);
return 0;
} |
// Java program to convert a // ternary number to decimal number class GFG{
// Function to convert a ternary // number to a decimal number static void convertToDecimal( int N)
{ System.out.print( "Decimal number of " +
N + " is: " );
// If the number is greater than 0,
// compute the decimal
// representation of the number
if (N != 0 )
{
int decimalNumber = 0 ,
i = 0 , remainder;
// Loop to iterate through
// the number
while (N != 0 )
{
remainder = N % 10 ;
N /= 10 ;
// Computing the decimal digit
decimalNumber += remainder *
Math.pow( 3 , i);
++i;
}
System.out.print(decimalNumber + "\n" );
}
else
System.out.print( "0" + "\n" );
} // Driver code public static void main(String[] args)
{ int Ternary = 10202202 ;
convertToDecimal(Ternary);
} } // This code is contributed by Rajput-Ji |
# Python3 program to convert a # ternary number to decimal number import math;
# Function to convert a ternary # number to a decimal number def convertToDecimal(N):
print ( "Decimal number of" , N, "is:" , end = " " );
# If the number is greater than 0,
# compute the decimal
# representation of the number
if (N ! = 0 ):
decimalNumber = 0 ;
i = 0 ;
remainder = 0 ;
# Loop to iterate through
# the number
while (N ! = 0 ):
remainder = N % 10 ;
N = N / / 10 ;
# Computing the decimal digit
decimalNumber + = remainder * math. pow ( 3 , i);
i + = 1 ;
print (decimalNumber);
else :
print ( "0" );
# Driver code Ternary = 10202202 ;
convertToDecimal(Ternary); # This code is contributed by Code_Mech |
// C# program to convert a ternary // number to decimal number using System;
class GFG{
// Function to convert a ternary // number to a decimal number static void convertToDecimal( int N)
{ Console.Write( "Decimal number of " +
N + " is: " );
// If the number is greater than
// 0, compute the decimal
// representation of the number
if (N != 0)
{
int decimalNumber = 0;
int i = 0, remainder;
// Loop to iterate through
// the number
while (N != 0)
{
remainder = N % 10;
N /= 10;
// Computing the decimal digit
decimalNumber += remainder *
( int )Math.Pow(3, i);
++i;
}
Console.Write(decimalNumber + "\n" );
}
else
Console.Write( "0" + "\n" );
} // Driver code public static void Main()
{ int Ternary = 10202202;
convertToDecimal(Ternary);
} } // This code is contributed by shivanisinghss2110 |
<script> // Javascript program to convert a ternary // number to decimal number // Function to convert a ternary // number to a decimal number function convertToDecimal(N)
{ document.write( "Decimal number of " +
N + " is: " );
// If the number is greater than
// 0, compute the decimal
// representation of the number
if (N != 0)
{
let decimalNumber = 0;
let i = 0, remainder;
// Loop to iterate through
// the number
while (N != 0)
{
remainder = N % 10;
N = parseInt(N / 10, 10);
// Computing the decimal digit
decimalNumber += remainder * Math.pow(3, i);
++i;
}
document.write(decimalNumber + "</br>" );
}
else
document.write( "0" + "</br>" );
} // Driver code let Ternary = 10202202; convertToDecimal(Ternary); // This code is contributed by divyesh072019 </script> |
Output:
Decimal number of 10202202 is: 2747
Time Complexity: O(log10N)
Auxiliary Space: O(1)