2 to the power of N in C without pow

Question

How can i calculate in C power of 2, without pow function?

For example, after keyboard input 4, the result to be 16?

I know that, for example, 2^5 can be typing similar like 2^1*2^5 (I don't know if this idea can help)

Answer 1

To calculate 2^N in C, use 1 << N.

If this may exceed the value representable in an int, use (Type) 1 << N, where Type is the integer type you want to use, such as unsigned long or uint64_t.

<< is the left-shift operator. It moves bits “left” in the bits that represent a number. Since numbers are represented in binary, moving bits left increases the powers of 2 they represent. Thus, 1₂ represents 1, 10₂ represents 2, 100₂ represents 4, and so on, so 1 shifted left N positions represents 2^N.

Answer 2

Numbers can be represented in binary form. For example, if integers are stored using 32 bits, 1 is stored like this:

00000000 00000000 00000000 00000001

And the value is the result of 1 x (2⁰)

If you do a left-shift operation your value will be stored as this:

00000000 00000000 00000000 00000010

That means that now the result is result of 1 x (2¹)

Bit used to store a type is sizeof(type)x8, because a byte is 8 bit.

So best method is to use shift:

The left-shift of 1 by exp is equivalent to 2 raised to exp. Shift operators must not be used for negative exponents in case of pow. The result is an undefined behaviour. Another case of undefined behavior is the one of shifting the number equal to or more than N, in case of that number is stored in N bits.

#include <stdio.h>
#include <stdlib.h>

int main() {
    int exp;
    printf("Please, insert exponent:\n");
    if (scanf("%d", &exp) != 1) {
        printf("ERROR: scanf\n");
        exit(EXIT_FAILURE);
    }
    if (exp < 0) {
        printf("ERROR: exponent must be >= 0\n");
        exit(EXIT_FAILURE);
    }
    printf("2^(%d) = %d\n", exp, 1 << exp);
    exit(EXIT_SUCCESS);
}

You can also do it creating a ricorsive function (int) -> int:

int my_pow(int exp) {
    If (exp < 0 ) {
        return -1;
    }
    if (exp == 0) {
        return 1;
    }
    if (exp > 0) {
        return 2 * my_pow(exp-1);
    }
}

Using it as main:

int main() {    
    int exp;
    scanf("%d" &exp);
    int res = my_pow(exp);
        if (res == -1) {
            printf("ERROR: Exponent must be equal or bigger than 0\n");
            exit(EXIT_FAILURE);
        } 
        printf("2^(%d) = %d", exp, res);
    return 0;
}