c-gcc, 70 bytes

Result

AC

Code [DL]

main(s){for(;gets(&s);putchar(48+!fmod(sqrt(strtol(&s,0,2)*8+1),1)));}

stdin

00000000
11010010
00001010
00101101
01101111
01001001
10011110
11100111
01000010
10011001
01011011
01001110
11011001
00011100
10001010
00000011
00000100
11100111
01010111
01101001
00001111
10101101
10100010
10010011
00000110
01111100
11011111
00000000
10111110
10111000
10101011
00011001
01010100
00000001
00110111
00100100
11111101
00110010
10001000
10110011
00010101
01101100
01100001
11000010
01101110
11001111
00001000
10001011
01110101
01111000

stdout

11110001111101010101100010011010011110101000000001

stderr

/tmp/code.c:1:1: warning: return type defaults to ‘int’ [-Wimplicit-int]
 main(s){for(;gets(&s);putchar(48+!fmod(sqrt(strtol(&s,0,2)*8+1),1)));}
 ^
/tmp/code.c: In function ‘main’:
/tmp/code.c:1:1: warning: type of ‘s’ defaults to ‘int’ [-Wimplicit-int]
/tmp/code.c:1:14: warning: implicit declaration of function ‘gets’ [-Wimplicit-function-declaration]
 main(s){for(;gets(&s);putchar(48+!fmod(sqrt(strtol(&s,0,2)*8+1),1)));}
              ^
/tmp/code.c:1:23: warning: implicit declaration of function ‘putchar’ [-Wimplicit-function-declaration]
 main(s){for(;gets(&s);putchar(48+!fmod(sqrt(strtol(&s,0,2)*8+1),1)));}
                       ^
/tmp/code.c:1:35: warning: implicit declaration of function ‘fmod’ [-Wimplicit-function-declaration]
 main(s){for(;gets(&s);putchar(48+!fmod(sqrt(strtol(&s,0,2)*8+1),1)));}
                                   ^
/tmp/code.c:1:35: warning: incompatible implicit declaration of built-in function ‘fmod’
/tmp/code.c:1:35: note: include ‘<math.h>’ or provide a declaration of ‘fmod’
/tmp/code.c:1:40: warning: implicit declaration of function ‘sqrt’ [-Wimplicit-function-declaration]
 main(s){for(;gets(&s);putchar(48+!fmod(sqrt(strtol(&s,0,2)*8+1),1)));}
                                        ^
/tmp/code.c:1:40: warning: incompatible implicit declaration of built-in function ‘sqrt’
/tmp/code.c:1:40: note: include ‘<math.h>’ or provide a declaration of ‘sqrt’
/tmp/code.c:1:45: warning: implicit declaration of function ‘strtol’ [-Wimplicit-function-declaration]
 main(s){for(;gets(&s);putchar(48+!fmod(sqrt(strtol(&s,0,2)*8+1),1)));}
                                             ^
/tmp/ccU8qbGM.o: In function `main':
code.c:(.text.startup+0x6c): warning: the `gets' function is dangerous and should not be used.

strace