c-gcc, 71 bytes

Result

AC

Code [DL]

main(s){for(;gets(&s);puts(fmod(sqrt(strtol(&s,0,2)*8+1),1)?"0":"1"));}

stdin

10001000
01111000
01100010
10011001
11010010
10101011
00100100
01111001
01011011
00110101
11111101
01100101
00011100
01000010
10111110
01001110
00000000
01000101
01110111
11011110
00001010
00110110
11100111
00000110
01101001
00000001
01010011
11010011
00110111
10111111
00101101
01011000
00000011
00010110
00000111
01100110
10110011
00011010
10100111
01011100
10101000
00010101
00110000
00001110
10010001
11010010
01111000
00001111
10011000
11100110

stdout

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

stderr

/tmp/code.c:1:1: warning: return type defaults to ‘int’ [-Wimplicit-int]
 main(s){for(;gets(&s);puts(fmod(sqrt(strtol(&s,0,2)*8+1),1)?"0":"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);puts(fmod(sqrt(strtol(&s,0,2)*8+1),1)?"0":"1"));}
              ^
/tmp/code.c:1:23: warning: implicit declaration of function ‘puts’ [-Wimplicit-function-declaration]
 main(s){for(;gets(&s);puts(fmod(sqrt(strtol(&s,0,2)*8+1),1)?"0":"1"));}
                       ^
/tmp/code.c:1:28: warning: implicit declaration of function ‘fmod’ [-Wimplicit-function-declaration]
 main(s){for(;gets(&s);puts(fmod(sqrt(strtol(&s,0,2)*8+1),1)?"0":"1"));}
                            ^
/tmp/code.c:1:28: warning: incompatible implicit declaration of built-in function ‘fmod’
/tmp/code.c:1:28: note: include ‘<math.h>’ or provide a declaration of ‘fmod’
/tmp/code.c:1:33: warning: implicit declaration of function ‘sqrt’ [-Wimplicit-function-declaration]
 main(s){for(;gets(&s);puts(fmod(sqrt(strtol(&s,0,2)*8+1),1)?"0":"1"));}
                                 ^
/tmp/code.c:1:33: warning: incompatible implicit declaration of built-in function ‘sqrt’
/tmp/code.c:1:33: note: include ‘<math.h>’ or provide a declaration of ‘sqrt’
/tmp/code.c:1:38: warning: implicit declaration of function ‘strtol’ [-Wimplicit-function-declaration]
 main(s){for(;gets(&s);puts(fmod(sqrt(strtol(&s,0,2)*8+1),1)?"0":"1"));}
                                      ^
/tmp/ccbWgGta.o: In function `main':
code.c:(.text.startup+0x6c): warning: the `gets' function is dangerous and should not be used.

strace