gistfile1.m

#import <Foundation/Foundation.h>

int intFromChar(char aChar, int notation) {
    // error
    if (!isalnum(aChar))
        return INT_MAX;
    
    int result = 0;
    
    if (isdigit(aChar)) // '0'-'9'
        result = aChar - 48;
    else                // 'a'-'z', 'A'-'Z'
        result = tolower(aChar) - 97 + 10;
    
    if (result >= notation)
        return INT_MAX;
    else
        return result;
}

int intFromString(NSString* aString, int notation) {
    // error
    if (notation > 10 + 26)
        return INT_MAX;
    
    int result = 0, flag = 1;
    
    int i = 0;
    if ([aString characterAtIndex:0] == '-') {
        flag = -1;
        i = 1;
    }
    
    for (; i < aString.length; i++) {
        int num = intFromChar([aString characterAtIndex:i], notation);
        if (num < notation)
            result += num * flag * pow(notation, aString.length - i - 1);
        else {
            result = INT_MAX;
            break;
        }
    }
    
    return result;
}

char charFromInt(int aNumber, int notation) {
    // error
    if (aNumber >= notation)
        return '\0';
    
    if (aNumber < 10)
        return aNumber + 48;
    else
        return aNumber + 97 - 10;
}

NSString* stringFromInt(int aNumber, int notation) {
    // error
    if (aNumber == INT_MAX)
        return @"error";
    
    NSString *numString = @"";
    int x = aNumber;
    
    if (x == 0)
        return @"0";
    else if (x < 0) {
        x = -x;
        numString = [numString stringByAppendingString:@"-"];
    }
    
    for (int i = floor(log(x)/log(notation)); i >= 0; i--) {
        int digit = pow(notation, i);
        char numChar = charFromInt(x / digit, notation);
        if (x / digit < notation)
            numString = [numString stringByAppendingFormat:@"%c", numChar];
        x = x % digit;
    }
    
    return numString;
}

NSString* convert(NSString* fromString, int fromNotation, int toNotation) {
    if (fromNotation < 1 || toNotation < 1 || fromNotation > 10 + 26 || toNotation > 10 + 26)
        return nil;
    
    int num = intFromString(fromString, fromNotation);
    return stringFromInt(num, toNotation);
}

int main(int argc, char **argv) {
    @autoreleasepool {
        NSLog(@"%@", convert(@"10", 10, 16));
    }
}