Un sistema numérico puede considerarse como una notación matemática de números que utiliza un conjunto de dígitos o símbolos. En palabras más simples, el sistema numérico es un método para representar números. Todo sistema numérico se identifica con la ayuda de su base o raíz.
Por ejemplo, los sistemas numéricos binarios , octales , decimales y hexadecimales se utilizan en la programación de microprocesadores . En este artículo, se analiza uno de esos sistemas numéricos.
Sistema numérico ternario:
si el valor base de un sistema numérico es 3, esta representación se conoce como representación ternaria . Los dígitos en este sistema son 0, 1 y 2 .
También existe un sistema numérico llamado Ternario Equilibrado que comprende los dígitos −1, 0 y +1 . La representación ternaria de un número es más compacta que la del sistema numérico binario.
Pasos para convertir decimal a ternario:
- Divide el número entre 3.
- Obtenga el cociente entero para la próxima iteración.
- Obtenga el resto para el dígito ternario.
- Repite los pasos hasta que el cociente sea igual a 0.
Por ejemplo: sea N = 101. La siguiente imagen ilustra la conversión paso a paso de 101 10 a la base-3.
A continuación se muestra la implementación de Decimal a Binario y Viceversa:
C++
// 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
// 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
<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>
Producción:
Ternary number of 2747 is: 10202202
Complejidad de tiempo: O (log 3 N)
Espacio Auxiliar: O(log 3 N)
Pasos para convertir ternario a decimal:
- Conecta cada dígito del número ternario con su correspondiente potencia de tres.
- Multiplica cada dígito por su correspondiente potencia de tres y suma todos los números que obtuviste.
Por ejemplo: sea N = 10202. La siguiente imagen ilustra la conversión paso a paso de 10202 3 a la base-10.
A continuación se muestra la implementación de Decimal a Binario y Viceversa:
C++
// 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
// 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
Javascript
<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>
Producción:
Decimal number of 10202202 is: 2747
Complejidad de tiempo: O (log 10 N)
Espacio Auxiliar: O(1)
Publicación traducida automáticamente
Artículo escrito por harsh_thoriya y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA