c-gcc, 86 bytes

Result

AC

Code [DL]

s[9];main(j,a,t){for(;gets(s);puts(&a))for(t=strtol(s,0,2),j=a=48;--j;)a+=j*j-j==t*2;}

stdin

10011001
01111000
00100101
00000000
01011011
10101101
00000001
00001010
10110001
00110111
11111101
00011100
00011001
10010011
10100000
01000010
00011111
00100100
11100111
10001000
00000011
00111110
00001011
00101000
01100011
01100110
00101100
00000110
11110000
00001111
10010111
10111110
00110111
01111101
10101011
01110110
00001010
00010101
11110010
00110101
11011101
11100100
01001110
01101001
10101111
00110010
11010010
00101101
11100101
11111110

stdout

1
1
0
1
1
0
1
1
0
1
1
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0

stderr

/tmp/code.c:1:1: warning: data definition has no type or storage class
 s[9];main(j,a,t){for(;gets(s);puts(&a))for(t=strtol(s,0,2),j=a=48;--j;)a+=j*j-j==t*2;}
 ^
/tmp/code.c:1:1: warning: type defaults to ‘int’ in declaration of ‘s’ [-Wimplicit-int]
/tmp/code.c:1:6: warning: return type defaults to ‘int’ [-Wimplicit-int]
 s[9];main(j,a,t){for(;gets(s);puts(&a))for(t=strtol(s,0,2),j=a=48;--j;)a+=j*j-j==t*2;}
      ^
/tmp/code.c: In function ‘main’:
/tmp/code.c:1:6: warning: type of ‘j’ defaults to ‘int’ [-Wimplicit-int]
/tmp/code.c:1:6: warning: type of ‘a’ defaults to ‘int’ [-Wimplicit-int]
/tmp/code.c:1:6: warning: type of ‘t’ defaults to ‘int’ [-Wimplicit-int]
/tmp/code.c:1:23: warning: implicit declaration of function ‘gets’ [-Wimplicit-function-declaration]
 s[9];main(j,a,t){for(;gets(s);puts(&a))for(t=strtol(s,0,2),j=a=48;--j;)a+=j*j-j==t*2;}
                       ^
/tmp/code.c:1:31: warning: implicit declaration of function ‘puts’ [-Wimplicit-function-declaration]
 s[9];main(j,a,t){for(;gets(s);puts(&a))for(t=strtol(s,0,2),j=a=48;--j;)a+=j*j-j==t*2;}
                               ^
/tmp/code.c:1:46: warning: implicit declaration of function ‘strtol’ [-Wimplicit-function-declaration]
 s[9];main(j,a,t){for(;gets(s);puts(&a))for(t=strtol(s,0,2),j=a=48;--j;)a+=j*j-j==t*2;}
                                              ^
/tmp/cc7DO259.o: In function `main':
code.c:(.text.startup+0x10): warning: the `gets' function is dangerous and should not be used.

strace