js-rhino, 113 bytes

Result

WA

Code [DL]

for(c=ew java.util.Scanner(java.lang.System.in);c.hasNext();)print(+!(Math.sqrt(8*parseInt(c.nextLine(),2)+1)%1))

stdin

01111011
11101010
10011001
01000000
10101011
00000110
01011011
00101000
01011010
11111111
00011100
01101001
11011101
11010010
00100100
00001111
01111000
00111011
00110111
10001100
11001010
01110100
00010101
00100100
00001010
01001110
00110100
00110110
01001110
00000011
11111101
01101010
01010000
00000000
01101111
00000001
00101101
10100100
11111001
01011111
11010000
00101001
01111111
11100111
01000010
10111110
00111010
00110001
10001000
00100110

stdout

stderr

js: "/volume/CODE", line 1: missing ; after for-loop initializer
js: for(c=ew java.util.Scanner(java.lang.System.in);c.hasNext();)print(+!(Math.sqrt(8*parseInt(c.nextLine(),2)+1)%1))
js: .............^
js: "/volume/CODE", line 1: syntax error
js: for(c=ew java.util.Scanner(java.lang.System.in);c.hasNext();)print(+!(Math.sqrt(8*parseInt(c.nextLine(),2)+1)%1))
js: ............................................................^
js: "/volume/CODE", line 1: Compilation produced 2 syntax errors.

strace