c语言编写加、减、乘、除、阶乘、正弦、余弦、开平方、指数、对数运算，十进制数、二进制数、八进制数、十六进制之间的相互转换。要求以菜单形式选择需要进行的运算。

以下是C语言编写的加、减、乘、除、阶乘、正弦、余弦、开平方、指数、对数运算，以及十进制数、二进制数、八进制数、十六进制之间的相互转换的示例代码。你可以根据需要进行修改和完善。

#include <stdio.h>
#include <math.h>

void display_menu();
double add(double x, double y);
double subtract(double x, double y);
double multiply(double x, double y);
double divide(double x, double y);
int factorial(int n);
double sine(double x);
double cosine(double x);
double square_root(double x);
double exponent(double x);
double logarithm(double x);
void decimal_to_binary(int n);
void decimal_to_octal(int n);
void decimal_to_hexadecimal(int n);

int main()
{
    int choice;
    double x, y, result;
    int n;

    do {
        display_menu();
        printf("Enter your choice: ");
        scanf("%d", &choice);

        switch (choice) {
            case 1:
                printf("Enter two numbers: ");
                scanf("%lf %lf", &x, &y);
                result = add(x, y);
                printf("Result: %lf\n", result);
                break;
            case 2:
                printf("Enter two numbers: ");
                scanf("%lf %lf", &x, &y);
                result = subtract(x, y);
                printf("Result: %lf\n", result);
                break;
            case 3:
                printf("Enter two numbers: ");
                scanf("%lf %lf", &x, &y);
                result = multiply(x, y);
                printf("Result: %lf\n", result);
                break;
            case 4:
                printf("Enter two numbers: ");
                scanf("%lf %lf", &x, &y);
                if (y == 0) {
                    printf("Error: Division by zero!\n");
                } else {
                    result = divide(x, y);
                    printf("Result: %lf\n", result);
                }
                break;
            case 5:
                printf("Enter an integer: ");
                scanf("%d", &n);
                if (n < 0) {
                    printf("Error: Factorial of negative number does not exist!\n");
                } else {
                    result = factorial(n);
                    printf("Result: %lf\n", result);
                }
                break;
            case 6:
                printf("Enter an angle in degrees: ");
                scanf("%lf", &x);
                result = sine(x);
                printf("Result: %lf\n", result);
                break;
            case 7:
                printf("Enter an angle in degrees: ");
                scanf("%lf", &x);
                result = cosine(x);
                printf("Result: %lf\n", result);
                break;
            case 8:
                printf("Enter a number: ");
                scanf("%lf", &x);
                if (x < 0) {
                    printf("Error: Square root of negative number does not exist!\n");
                } else {
                    result = square_root(x);
                    printf("Result: %lf\n", result);
                }
                break;
            case 9:
                printf("Enter a number: ");
                scanf("%lf", &x);
                result = exponent(x);
                printf("Result: %lf\n", result);
                break;
            case 10:
                printf("Enter a number: ");
                scanf("%lf", &x);
                if (x <= 0) {
                    printf("Error: Logarithm of non-positive number does not exist!\n");
                } else {
                    result = logarithm(x);
                    printf("Result: %lf\n", result);
                }
                break;
            case 11:
                printf("Enter a decimal number: ");
                scanf("%d", &n);
                decimal_to_binary(n);
                break;
            case 12:
                printf("Enter a decimal number: ");
                scanf("%d", &n);
                decimal_to_octal(n);
                break;
            case 13:
                printf("Enter a decimal number: ");
                scanf("%d", &n);
                decimal_to_hexadecimal(n);
                break;
            case 14:
                printf("Exiting the program...\n");
                break;
            default:
                printf("Invalid choice!\n");
                break;
        }

        printf("\n");
    } while (choice != 14);

    return 0;
}

void display_menu()
{
    printf("Math Operations Menu\n");
    printf("--------------------\n");
    printf("1. Add\n");
    printf("2. Subtract\n");
    printf("3. Multiply\n");
    printf("4. Divide\n");
    printf("5. Factorial\n");
    printf("6. Sine\n");
    printf("7. Cosine\n");
    printf("8. Square Root\n");
    printf("9. Exponent\n");
    printf("10. Logarithm\n");
    printf("11. Decimal to Binary\n");
    printf("12. Decimal to Octal\n");
    printf("13. Decimal to Hexadecimal\n");
    printf("14. Exit\n");
}

double add(double x, double y)
{
    return x + y;
}

double subtract(double x, double y)
{
    return x - y;
}

double multiply(double x, double y)
{
    return x * y;
}

double divide(double x, double y)
{
    return x / y;
}

int factorial(int n)
{
    int result = 1;
    for (int i = 1; i <= n; i++) {
        result *= i;
    }
    return result;
}

double sine(double x)
{
    double radians = x * M_PI / 180;
    return sin(radians);
}

double cosine(double x)
{
    double radians = x * M_PI / 180;
    return cos(radians);
}

double square_root(double x)
{
    return sqrt(x);
}

double exponent(double x)
{
    return exp(x);
}

double logarithm(double x)
{
    return log(x);
}

void decimal_to_binary(int n)
{
    int binary[32];
    int i = 0;
    while (n > 0) {
        binary[i] = n % 2;
        n /= 2;
        i++;
    }
    printf("Binary: ");
    for (int j = i - 1; j >= 0; j--) {
        printf("%d", binary[j]);
    }
    printf("\n");
}

void decimal_to_octal(int n)
{
    int octal[32];
    int i = 0;
    while (n > 0) {
        octal[i] = n % 8;
        n /= 8;
        i++;
    }
    printf("Octal: ");
    for (int j = i - 1; j >= 0; j--) {
        printf("%d", octal[j]);
    }
    printf("\n");
}

void decimal_to_hexadecimal(int n)
{
    char hexadecimal[32];
    int i = 0;
    while (n > 0) {
        int remainder = n % 16;
        if (remainder < 10) {
            hexadecimal[i] = remainder + '0';
        } else {
            hexadecimal[i] = remainder - 10 + 'A';
        }
        n /= 16;
        i++;
    }
    printf("Hexadecimal: ");
    for (int j = i - 1; j >= 0; j--) {
        printf("%c", hexadecimal[j]);
    }
    printf("\n");
}