First of all, remember to put your own code in code tags, instead of poor Shabbir having to do it. He ain't yo' mama.

What you get from input is going to be a character (multiple characters, actually, a string), not an integer. That's why I mentioned conversions. Give this a shot (note the cases are characters, not integers):
Code:
#include <stdio.h>

int ohHell (char *trouble)
{
    fprintf (stderr, "%s\n", trouble);
    return EOF;
}
int main()
{
	char input[256];
	char base [256];

    printf("Please enter positive number: ");
    if (!fgets (input, 30, stdin)) return ohHell ("Failure on input");

	printf("Please ener the base (1->binary, 2->octal, 3->decimal, 4->hexadecimal): ");
    if (!fgets (base, 30, stdin)) return ohHell ("Failure on input");

    printf ("You selected ");
    switch (base[0])
    {
    case '1':
        printf ("binary");
        break;
    case '2':
        printf ("octal");
        break;
    case '3':
        printf ("decimal");
        break;
    case '4':
        printf ("hex");
        break;
    default:
        printf ("an invalid character");
    }
    printf ("\n");
    return 0;
}