三进制数制或基数3

可以使用一组数字或符号将数字系统视为数字的数学符号。用简单的话来说，数字系统是一种表示数字的方法。每个数字系统都通过其基数或基数来识别。
例如，在微处理器编程中使用Binary ， Octal ， Decimal和Hexadecimal Number系统。在本文中，将讨论一个这样的数字系统。
三元数系统：
如果数字系统的基值为3，则此表示形式称为三进制表示形式。该系统中的数字为0，1和2 。
还有一个称为“平衡三进制”的数字系统，其中包括数字-1、0和+1 。数字的三进制表示比二进制数字系统紧凑。

将十进制转换为三进制的步骤：

1. 将数字除以3。
2. 获取下一次迭代的整数商。
3. 获取三进制数的余数。
4. 重复这些步骤，直到商等于0。

例如： N =101。下图说明了将101 ¹⁰逐步转换为base-3的过程。

以下是十进制转二进制和反Versa的实现：

C++

// C++ program to convert decimal
// number to ternary number
 
#include 
#include 
#include 
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

// 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

# 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#

// 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

Javascript

    // 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.

输出：

Ternary number of 2747 is: 10202202

将三进制转换为十进制的步骤：

1. 将三进制数中的每个数字与其对应的3的幂连接起来。
2. 将每个数字乘以其相应的三的幂，然后将所有得到的数字相加。

例如： N =10202。下图说明了10202 _3到10的逐步转换_。

_{以下是十进制转二进制和反Versa的实现：}

C++

// C++ program to convert a
// ternary number to decimal number
 
#include 
#include 
#include 
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

// 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

# 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＃

// 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

_输出：  

Decimal number of 10202202 is: 2747