js-rhino, 94 bytes

Result

WA

Code [DL]

for(a=new java.util.Scanner(java.lang.System.in);q=a.nextLine();print(+!(`0b${q}001`**.5%1)));

stdin

00110111
00000001
01011011
10101011
11100010
00000011
10111111
01101001
01110010
01001110
11100111
00100100
10010010
01001011
01111000
00110001
11010010
10111110
10110101
00011100
11101011
11111101
00010101
10111000
00110111
11110010
11111001
00000110
10101001
10011000
01010111
00001111
10011001
00101101
00001010
00000000
01110000
00110010
01000010
01010100
00110101
10000010
11100100
00011100
01001010
11011110
11101110
11011011
10001000
11010101

stdout

stderr

js: "/volume/CODE", line 1: illegal character
js: for(a=new java.util.Scanner(java.lang.System.in);q=a.nextLine();print(+!(`0b${q}001`**.5%1)));
js: .........................................................................^
js: "/volume/CODE", line 1: missing ) in parenthetical
js: for(a=new java.util.Scanner(java.lang.System.in);q=a.nextLine();print(+!(`0b${q}001`**.5%1)));
js: ...........................................................................^
js: "/volume/CODE", line 1: illegal character
js: for(a=new java.util.Scanner(java.lang.System.in);q=a.nextLine();print(+!(`0b${q}001`**.5%1)));
js: ...................................................................................^
js: "/volume/CODE", line 1: syntax error
js: for(a=new java.util.Scanner(java.lang.System.in);q=a.nextLine();print(+!(`0b${q}001`**.5%1)));
js: .....................................................................................^
js: "/volume/CODE", line 1: Compilation produced 4 syntax errors.

strace