将数字从 2 进制 (二进制) 转换为 6 进制

2024年8月28日 | 阅读 7 分钟

本文讨论了将二进制数转换为六进制数的实际实现

问题 - 问题是将给定的二进制数转换为其等效的六进制数。

例如

Input 1: N = 1101101 = 109₁₀
Output = 301 (301₆ = 3 x 6² + 0 x 6¹ + 1 x 6⁰ = 3 x 36 + 1 = 109)

Input 2: N = 1110111 = 119₁₀
Output = 315 (315₆ = 3 x 6² + 1 x 6¹ + 5 x 6⁰ = 3 x 36 + 1 x 6 + 5 x 1 = 119)

思路和方法

获得所需结果的简单想法是首先将给定的二进制数转换为其等效的十进制数，然后将其转换为其等效的六进制数。

现在让我们了解解决问题所涉及的工作/函数

binaryToDecimal() 函数的工作原理

所需函数的伪代码如下

二进制转十进制 (Int n) // 其中 n 是二进制输入

{
a.	Int dec = 0; // decimal variable to store the result of the function
b.	Int pv = 1; // Pv is the place value variable

c.	While n is greater than 0
d.	{
e.	dec = dec + pv x (n % 10)
f.	pv = pv x 10
g.	n = n / 10
h.	}

i.	decimalToBase6(dec) // Calling the Decimal to Base 6 function to get the output
}

decimalToBase6() 函数的工作原理

所需函数的伪代码如下

十进制转六进制 (Int dec) // 其中 dec 是十进制输入

{
a.	Int output = 0; // output variable to store the result of the function
b.	Int pv = 1; // Pv is the place value variable

c.	While dec is greater than 0
d.	{
e.	output = output + pv x (n % 6)
f.	pv = pv x 10
g.	dec = dev / 6
h.	}
i.	Print the output and exit
}

让我们举个例子进一步理解

设 n = 1101，当我们调用二进制转十进制函数时，它将首先创建一些变量并将它们初始化为某个值。这里，dec = 0，pv = 1 被创建。现在，检查 while 循环条件。这里，n = 1101，大于零，所以，我们进入第一次迭代。

第一次迭代

dec = dec + pv * (n % 10) = 0 + 1 * (1) = 0 + 1 = 1
pv = pv * 2 = 1 * 2 = 2
n = n /10 = 1101 / 10

第二次迭代

dec = dec + pv * (n % 10) = 1 + 2 * (0) = 1 + 0 = 1
pv = pv * 2 = 2 * 2 = 4
n = n / 10 = 110 / 10 = 11

第三次迭代

dec = dec + pv * (n % 10) = 1 + 4 * (1) = 1 + 4 = 5
pv = pv * 2 = 4 * 2 = 8
n = n / 10 = 11 / 10 = 1

第 4 次迭代

dec = dec + pv * (n % 10) = 5 + 8 * (1) = 5 + 8 = 13
pv = pv * 2 = 8 * 2 = 16
n = n / 10 = 1 / 10 = 0

在这里，while 循环将终止，因为 n 现在等于零。现在，它将调用 decimalToBase6(dec) 函数并将 dec = 13 传递给它。

当调用 decimaltToBase6 函数时，它创建了 pv = 1 和 output = 0。dec = 13 被传递给该函数，它大于零，因此满足 while 循环条件。让我们逐个查看每个迭代

第一次迭代

output = output + pv * (dec % 6) = 0 + 1 * (13 % 6) = 0 + 1 * 1 = 1
pv = pv * 10 = 1 * 10 = 10
dec = dec / 6 = 13 / 6 = 2

第二次迭代

output = output + pv * (dec % 6) = 1 + 10 (2 % 6) = 1 + 10 * 2 = 21
pv = pv * 10 = 10 * 10 = 100
dec = dec / 6 = 2 / 6 = 0

这里，dec 现在等于零。所以，在下一次迭代中，while 循环的条件将失败，它将打印输出并退出程序。

上述问题的实际实现

1. Java 实现

package javatpoint;

public class BinaryToBase6 {

    // Function To convert the decimal number into its equivalent number in base 6
    public static void decimalToBase6(int dec) {
        // Output variable will store the result
        int output = 0;
        int pv = 1;
        // The while loop terminates when the dec number becomes equal to zero
        while (dec > 0) {
            output = output + pv * (dec % 6);
            dec = dec / 6;
            pv = pv * 10;
        }
        System.out.println(output);
    }

    // Function to convert the binary number into its equivalent decimal number
    public static void binaryToDecimal(int n) {
        // The dec variable will store the decimal number
        int dec = 0;
        int pv = 1;
        int temp = n;
        // The while loop terminates when the temp (Binary number) becomes equal to zero
        while (temp > 0) {
            dec = dec + pv * (temp % 10);
            temp = temp / 10;
            pv = 2 * pv;
        }
        System.out.print("The Base6 equivalent of " + n + " = ");
        // Calling the function to convert the dec into base6 number
        decimalToBase6(dec);
    }

    public static void main(String[] args) {
        // Calling the function and passing a binary number with each function call
        binaryToDecimal(1101101);
        binaryToDecimal(1110111);
        binaryToDecimal(1010111);
        binaryToDecimal(1101111);
    }

}

示例输出

The Base6 equivalent of 1101101 = 301
The Base6 equivalent of 1110111 = 315
The Base6 equivalent of 1010111 = 223
The Base6 equivalent of 1101111 = 303

2. C++ 实现

#include <iostream>
using namespace std;

// Function To convert a decimal number into its equivalent number in base 6
void decimalToBase6(int dec)
{
    // Output variable will store the result
    int output = 0;
    int pv = 1;
    // The while loop terminates when the dec number becomes equal to zero
    while (dec > 0)
    {
        output = output + pv * (dec % 6);
        dec = dec / 6;
        pv = pv * 10;
    }
    cout << output << endl;
}

// Function to convert a binary number into its equivalent decimal number
void binaryToDecimal(int n)
{
    // The dec variable will store the decimal number
    int dec = 0;
    int pv = 1;
    int temp = n;
    // The while loop terminates when the temp (Binary number) becomes equal to zero
    while (temp > 0)
    {
        dec = dec + pv * (temp % 10);
        temp = temp / 10;
        pv = 2 * pv;
    }
    cout << "The Base6 equivalent of " << n << " = ";
    // Calling the function to convert the dec into base6 number
    decimalToBase6(dec);
}

int main()
{
    // Calling the function and passing a binary number with each function call
    binaryToDecimal(11011011);
    binaryToDecimal(10110111);
    binaryToDecimal(10110111);
    binaryToDecimal(11011011);

    return 0;
}

示例输出

The Base6 equivalent of 11011011 = 1003
The Base6 equivalent of 10110111 = 503 
The Base6 equivalent of 10110111 = 503
The Base6 equivalent of 11011011 = 1003

3. C 语言实现

#include <stdio.h>

// Function To convert a decimal number into its equivalent number in base 6
void decimalToBase6(int dec)
{
    // Output variable will store the result
    int output = 0;
    int pv = 1;
    // The while loop terminates when the dec number becomes equal to zero
    while (dec > 0)
    {
        output = output + pv * (dec % 6);
        dec = dec / 6;
        pv = pv * 10;
    }
    printf("%d\n", output);
}

// Function to convert a binary number into its equivalent decimal number
void binaryToDecimal(int n)
{
    // The dec variable will store the decimal number
    int dec = 0;
    int pv = 1;
    int temp = n;
    // The while loop terminates when the temp (Binary number) becomes equal to zero
    while (temp > 0)
    {
        dec = dec + pv * (temp % 10);
        temp = temp / 10;
        pv = 2 * pv;
    }
    printf("The Base6 equivalent of %d = ", n);
    // Calling the function to convert the dec into base6 number
    decimalToBase6(dec);
}

int main()
{
    // Calling the function and passing a binary number with each function call
    binaryToDecimal(101010);
    binaryToDecimal(111101);
    binaryToDecimal(101101);
    binaryToDecimal(111010);

    return 0;
}

示例输出

The Base6 equivalent of 101010 = 110
The Base6 equivalent of 111101 = 141
The Base6 equivalent of 101101 = 113
The Base6 equivalent of 111010 = 134

4. Python 实现

# Function To convert a decimal number into its equivalent number in base 6
def decToBase6(dec):
    pv = 1
    output = 0  # Output variable will store the base6 equivalent of the given binary number

    # The while loop terminates when the dec number becomes equal to zero
    while(dec > 0):
        output = output + pv*(dec % 6)
        pv = pv * 10
        dec = dec // 6  # Integer Division

    print(output)

# Function to convert a binary number into its equivalent decimal number

def binaryToDecimal(n):
    # dec variable will store the decimal equivalent of the given binary number
    dec = 0
    pv = 1
    temp = n

    # The while loop terminates when the temp (Binary number) becomes equal to zero
    while(temp > 0):
        dec = dec + pv*(temp % 10)
        pv = pv * 2
        temp = temp//10  # Integer Division
    print(f"The base6 equivalent of {n} = ", end="")
    decToBase6(dec)

# Calling the function and passing a binary number with each function call
binaryToDecimal(1010101)
binaryToDecimal(1111010)
binaryToDecimal(1011011)
binaryToDecimal(1110100)

示例输出

The base6 equivalent of 1010101 = 221
The base6 equivalent of 1111010 = 322
The base6 equivalent of 1011011 = 231
The base6 equivalent of 1110100 = 312

下一主题缓存一致性

将数字从 2 进制 (二进制) 转换为 6 进制

问题 - 问题是将给定的二进制数转换为其等效的六进制数。

思路和方法

上述问题的实际实现

1. Java 实现

2. C++ 实现

3. C 语言实现

4. Python 实现

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将数字从 2 进制 (二进制) 转换为 6 进制

问题 - 问题是将给定的二进制数转换为其等效的六进制数。

思路和方法

上述问题的实际实现

1. Java 实现

2. C++ 实现

3. C 语言实现

4. Python 实现

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