c-gcc, 115 bytes

Result

AC

Code [DL]

int i,a,b;main(){for(;a<50;a++){for(b=i=0;b<9;b++,i+=getchar()&1,i*=2);i/=4;for(b=0;i>0;)i-=b++;putchar(i?48:49);}}

stdin

01000111
01101100
01011011
11010010
00111010
11001010
00110111
00101111
11000111
00001111
11000110
10101011
00011100
00000000
10111110
00010101
00100100
00011000
10001000
01101001
00010000
11011111
01000010
11111010
10011001
00101000
10010101
11000101
11000100
00101101
01001110
11101011
00101101
00011001
00001001
00100101
00000011
01100001
11111101
01110110
00000110
00000000
01111000
10011100
10101101
00001010
00001110
00000001
11100111
00111110

stdout

00110010010111111011001010000110100010101110010110

stderr

/tmp/code.c:1:11: warning: return type defaults to ‘int’ [-Wimplicit-int]
 int i,a,b;main(){for(;a<50;a++){for(b=i=0;b<9;b++,i+=getchar()&1,i*=2);i/=4;for(b=0;i>0;)i-=b++;putchar(i?48:49);}}
           ^
/tmp/code.c: In function ‘main’:
/tmp/code.c:1:54: warning: implicit declaration of function ‘getchar’ [-Wimplicit-function-declaration]
 int i,a,b;main(){for(;a<50;a++){for(b=i=0;b<9;b++,i+=getchar()&1,i*=2);i/=4;for(b=0;i>0;)i-=b++;putchar(i?48:49);}}
                                                      ^
/tmp/code.c:1:97: warning: implicit declaration of function ‘putchar’ [-Wimplicit-function-declaration]
 int i,a,b;main(){for(;a<50;a++){for(b=i=0;b<9;b++,i+=getchar()&1,i*=2);i/=4;for(b=0;i>0;)i-=b++;putchar(i?48:49);}}
                                                                                                 ^

strace