c-gcc, 83 bytes

Result

AC

Code [DL]

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

stdin

10000101
00000001
01000101
00111100
00011010
00001111
11111111
11001110
00101110
00011100
00000100
01011011
01000010
01111000
00010010
10000001
10011001
11000101
00010101
10101011
00001010
00000110
10100000
01101110
11100111
00110111
00000110
11111001
10111110
01001110
11101100
01101001
00101100
00111111
11011100
00000011
10010110
01101111
00001101
11111101
01001110
00000000
11111110
00101101
01110000
11010010
10001000
01001011
00100100
01011001

stdout

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

stderr

/tmp/code.c:1:1: warning: return type defaults to ‘int’ [-Wimplicit-int]
 main(j,s,a){for(;gets(&s);puts(&a))for(s=strtol(&s,0,2),j=a=48;--j;)a+=j*j-j==s*2;}
 ^
/tmp/code.c: In function ‘main’:
/tmp/code.c:1:1: warning: type of ‘j’ defaults to ‘int’ [-Wimplicit-int]
/tmp/code.c:1:1: warning: type of ‘s’ defaults to ‘int’ [-Wimplicit-int]
/tmp/code.c:1:1: warning: type of ‘a’ defaults to ‘int’ [-Wimplicit-int]
/tmp/code.c:1:18: warning: implicit declaration of function ‘gets’ [-Wimplicit-function-declaration]
 main(j,s,a){for(;gets(&s);puts(&a))for(s=strtol(&s,0,2),j=a=48;--j;)a+=j*j-j==s*2;}
                  ^
/tmp/code.c:1:27: warning: implicit declaration of function ‘puts’ [-Wimplicit-function-declaration]
 main(j,s,a){for(;gets(&s);puts(&a))for(s=strtol(&s,0,2),j=a=48;--j;)a+=j*j-j==s*2;}
                           ^
/tmp/code.c:1:42: warning: implicit declaration of function ‘strtol’ [-Wimplicit-function-declaration]
 main(j,s,a){for(;gets(&s);puts(&a))for(s=strtol(&s,0,2),j=a=48;--j;)a+=j*j-j==s*2;}
                                          ^
/tmp/cc9YxGmJ.o: In function `main':
code.c:(.text.startup+0x14): warning: the `gets' function is dangerous and should not be used.

strace