c-gcc, 83 bytes

Result

WA

Code [DL]

#include <math.h>
float a;main(){while(scanf("%b",a))putchar(sqrt(a*8+1)%2==1+48);}

stdin

01001011
10010011
00110111
01001111
01111000
01011001
00101111
10101001
01101100
11000011
01100011
00100100
01001110
10000011
01001100
01000010
00001010
11111101
01011011
00001111
00100010
10101011
00011100
11000101
11100000
10011001
00000000
11100101
10001000
01011111
01101001
11100111
00101101
00000010
10111110
11011011
01001110
00100100
00000001
11100001
11010010
00111000
01110010
01010011
11010111
00101000
00011101
00000011
00000110
00010101

stdout

stderr

/tmp/code.c:2:9: warning: return type defaults to ‘int’ [-Wimplicit-int]
 float a;main(){while(scanf("%b",a))putchar(sqrt(a*8+1)%2==1+48);}
         ^
/tmp/code.c: In function ‘main’:
/tmp/code.c:2:22: warning: implicit declaration of function ‘scanf’ [-Wimplicit-function-declaration]
 float a;main(){while(scanf("%b",a))putchar(sqrt(a*8+1)%2==1+48);}
                      ^
/tmp/code.c:2:22: warning: incompatible implicit declaration of built-in function ‘scanf’
/tmp/code.c:2:22: note: include ‘<stdio.h>’ or provide a declaration of ‘scanf’
/tmp/code.c:2:28: warning: unknown conversion type character ‘b’ in format [-Wformat=]
 float a;main(){while(scanf("%b",a))putchar(sqrt(a*8+1)%2==1+48);}
                            ^
/tmp/code.c:2:28: warning: too many arguments for format [-Wformat-extra-args]
/tmp/code.c:2:36: warning: implicit declaration of function ‘putchar’ [-Wimplicit-function-declaration]
 float a;main(){while(scanf("%b",a))putchar(sqrt(a*8+1)%2==1+48);}
                                    ^
/tmp/code.c:2:55: error: invalid operands to binary % (have ‘double’ and ‘int’)
 float a;main(){while(scanf("%b",a))putchar(sqrt(a*8+1)%2==1+48);}
                                                       ^
/home/esolang/bin/c-gcc: line 6: /tmp/code: No such file or directory
rm: cannot remove '/tmp/code': No such file or directory

strace