c-gcc, 73 bytes

Result

WA

Code [DL]

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

stdin

10110001
00100000
00101111
00111100
00000000
10001000
00001010
00101000
01011100
11100111
10101011
00110111
00101101
00000110
11001011
11111101
10110010
11010001
00011001
11000001
00001111
01011011
11001100
01001110
11000010
10111110
00001010
01101111
10010101
00110111
11011010
00000100
01000110
11010010
11001010
00011011
10010100
01101001
00010101
00011100
00101100
01000010
10011001
00100100
10110111
11111011
00000011
01111000
00000001
01111010

stdout

stderr

/tmp/code.c:1:1: warning: return type defaults to ‘int’ [-Wimplicit-int]
 main(s,a){for(;gets(&s);a=sqrt(s),a=48+a*a==s,puts(&a))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=sqrt(s),a=48+a*a==s,puts(&a))s=strtol(&s,0,2);}
                ^
/tmp/code.c:1:27: warning: implicit declaration of function ‘sqrt’ [-Wimplicit-function-declaration]
 main(s,a){for(;gets(&s);a=sqrt(s),a=48+a*a==s,puts(&a))s=strtol(&s,0,2);}
                           ^
/tmp/code.c:1:27: warning: incompatible implicit declaration of built-in function ‘sqrt’
/tmp/code.c:1:27: note: include ‘<math.h>’ or provide a declaration of ‘sqrt’
/tmp/code.c:1:47: warning: implicit declaration of function ‘puts’ [-Wimplicit-function-declaration]
 main(s,a){for(;gets(&s);a=sqrt(s),a=48+a*a==s,puts(&a))s=strtol(&s,0,2);}
                                               ^
/tmp/code.c:1:58: warning: implicit declaration of function ‘strtol’ [-Wimplicit-function-declaration]
 main(s,a){for(;gets(&s);a=sqrt(s),a=48+a*a==s,puts(&a))s=strtol(&s,0,2);}
                                                          ^
/tmp/ccYjwEAS.o: In function `main':
code.c:(.text.startup+0x63): warning: the `gets' function is dangerous and should not be used.

strace