Using modulo for negative values
Simply use modulo

#include &lt;stdio.h&gt;

int main(){
   for (int i = -23;i&lt;23;i++) printf("%d    %d\n",i,i%11);
   return 0;
}


all modern C variants should work the same way https://en.wikipedia.org/wiki/Modulo_operation (result have same sign as divident):

-23 -1
-22 0
-21 -10
-20 -9
-19 -8
-18 -7
-17 -6
-16 -5
-15 -4
-14 -3
-13 -2
-12 -1
-11 0
-10 -10
-9  -9
-8  -8
-7  -7
-6  -6
-5  -5
-4  -4
-3  -3
-2  -2
-1  -1
0   0
1   1
2   2
3   3
4   4
5   5
6   6
7   7
8   8
9   9
10  10
11  0
12  1
13  2
14  3
15  4
16  5
17  6
18  7
19  8
20  9
21  10
22  0




for new formulation of request fixed by @Gerben suggestion

if you want monotonic 0..10 sequencies, add 11, if result is negative :

#include &lt;stdio.h&gt;

int main(){
for (int i = -23;i&lt;23;i++)
    {
    int x= i%11 ;
    x += x&lt;0?11:0;
    printf("    %d  %d\n",i,x);
    };
return 0;
}


results in 

-23 10
-22 0
-21 1
-20 2
-19 3
-18 4
-17 5
-16 6
-15 7
-14 8
-13 9
-12 10
-11 0
-10 1
-9  2
-8  3
-7  4
-6  5
-5  6
-4  7
-3  8
-2  9
-1  10
0   0
1   1
2   2
3   3
4   4
5   5
6   6
7   7
8   8
9   9
10  10
11  0
12  1
13  2
14  3
15  4
16  5
17  6
18  7
19  8
20  9
21  10
22  0