c-gcc, 73 bytes

Result

WA

Code [DL]

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

stdin

00001111
10000001
00010111
10111110
01011100
00010101
10001000
00100100
01101001
10101011
11001010
10000111
10010001
01011011
00100100
01100001
10010100
11011100
00101101
00000011
01111000
00001010
11111101
11110110
00110111
10111010
01110011
01000010
00111011
11100111
00000000
01111111
00001101
01010100
00011100
11001110
11000001
10110100
00000001
10010101
01011011
01010110
10011010
10011110
00000110
01010101
11010010
01001110
01010010
10011001

stdout

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

stderr

/tmp/code.c:1:1: warning: return type defaults to ‘int’ [-Wimplicit-int]
 main(s,a){for(;gets(&s);a=48+(a*a==s),puts(&a))a=sqrt(s=strtol(&s,0,2));}
 ^
/tmp/code.c: In function ‘main’:
/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:1:16: warning: implicit declaration of function ‘gets’ [-Wimplicit-function-declaration]
 main(s,a){for(;gets(&s);a=48+(a*a==s),puts(&a))a=sqrt(s=strtol(&s,0,2));}
                ^
/tmp/code.c:1:39: warning: implicit declaration of function ‘puts’ [-Wimplicit-function-declaration]
 main(s,a){for(;gets(&s);a=48+(a*a==s),puts(&a))a=sqrt(s=strtol(&s,0,2));}
                                       ^
/tmp/code.c:1:50: warning: implicit declaration of function ‘sqrt’ [-Wimplicit-function-declaration]
 main(s,a){for(;gets(&s);a=48+(a*a==s),puts(&a))a=sqrt(s=strtol(&s,0,2));}
                                                  ^
/tmp/code.c:1:50: warning: incompatible implicit declaration of built-in function ‘sqrt’
/tmp/code.c:1:50: note: include ‘<math.h>’ or provide a declaration of ‘sqrt’
/tmp/code.c:1:57: warning: implicit declaration of function ‘strtol’ [-Wimplicit-function-declaration]
 main(s,a){for(;gets(&s);a=48+(a*a==s),puts(&a))a=sqrt(s=strtol(&s,0,2));}
                                                         ^
/tmp/ccgUoWYS.o: In function `main':
code.c:(.text.startup+0x63): warning: the `gets' function is dangerous and should not be used.

strace