Arduino - Writing int array with for loop doesn't work - arduino

Question

I am a college student so I'm still learning a lot. I ran into something interesting while making a project. I have this segment of code that works when it isn't placed in a for loop, but doesn't work when it is. I just want to understand why. Here is my code:
void setup() {
Serial.begin(9600);
int a[8];
for(int i=0;i<8;i++) {
a[i]=pow(2,i);
}
for(int i=0;i<8;i++) {
Serial.print(a[i]);
}
}
void loop() {
}
Here is the same code written without the first for loop (where the data gets written into the array):
void setup() {
Serial.begin(9600);
int a[8];
a[0]=pow(2,0);
a[1]=pow(2,1);
a[2]=pow(2,2);
a[3]=pow(2,3);
a[4]=pow(2,4);
a[5]=pow(2,5);
a[6]=pow(2,6);
a[7]=pow(2,7);
for(int i=0;i<8;i++) {
Serial.print(a[i]);
}
}
void loop() {
}
The first code outputs:
1
2
3
7
15
31
63
127
While the second code outputs:
1
2
4
8
16
32
64
128
Does anybody know? I really want to know why.

Answer 1

You are experiencing floating point round off. 2^4 will actually give you a value closer to 15.9999 and when this is assigned to an int, it truncates the decimal to 15. I would suggest doing bit shift operations when using powers of 2, such that:
for(int i=0;i<8;i++)
{
a[i]=(1 << i);
}
If you want to read up on bit shifting, look here.
If you want to know more about the floating point round off, look here.
Additionally if you wanted just a quick fix to your code closer to what you have, I believe this will also work:
for(int i=0;i<8;i++)
{
a[i]= (int) round( pow(2, i) );
}
This will round the floating result properly before casting it to an int.