c-gcc, 109 bytes

Result

AC

Code [DL]

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

stdin

10000100
00000011
00000001
11110001
11100111
11111101
10011001
10010011
10011011
00010100
10100101
10101011
01010110
11010101
01011100
01101001
00001000
00101101
01100100
00110111
11100010
10001111
10110101
00000000
00100100
11100001
00001010
00010101
11001000
00010101
10001000
00000000
11011100
00000110
01111000
00101010
01011011
00011100
01000011
11111010
11010010
01000010
01001110
10111111
01110111
01100111
11000001
10011000
10111110
00001111

stdout

01101110000100010101000110110111011011001110000011

stderr

/tmp/code.c:1:11: warning: return type defaults to ‘int’ [-Wimplicit-int]
 int i,a,b;main(){for(;a<50;a++){i=0;b=9;while(b--)i=i*2|getchar()&1;i/=2;while(i>0)i-=++b;putchar(i?48:49);}}
           ^
/tmp/code.c: In function ‘main’:
/tmp/code.c:1:57: warning: implicit declaration of function ‘getchar’ [-Wimplicit-function-declaration]
 int i,a,b;main(){for(;a<50;a++){i=0;b=9;while(b--)i=i*2|getchar()&1;i/=2;while(i>0)i-=++b;putchar(i?48:49);}}
                                                         ^
/tmp/code.c:1:66: warning: suggest parentheses around arithmetic in operand of ‘|’ [-Wparentheses]
 int i,a,b;main(){for(;a<50;a++){i=0;b=9;while(b--)i=i*2|getchar()&1;i/=2;while(i>0)i-=++b;putchar(i?48:49);}}
                                                                  ^
/tmp/code.c:1:91: warning: implicit declaration of function ‘putchar’ [-Wimplicit-function-declaration]
 int i,a,b;main(){for(;a<50;a++){i=0;b=9;while(b--)i=i*2|getchar()&1;i/=2;while(i>0)i-=++b;putchar(i?48:49);}}
                                                                                           ^

strace