js-rhino, 81 bytes

Result

WA

Code [DL]

for(;;)java.lang.System c;print(+!(Math.sqrt(8*parseInt(c.in.readLine(),2)+1)%1))

stdin

10011110
10011001
01100101
00000110
01001101
00110111
01010101
10011001
01001110
00010100
11001101
11010100
01010100
00001011
00011001
10101001
00100100
10101110
01111000
11111100
00000011
10111110
10110000
00000001
11111101
01000110
10001000
11110100
01110111
11000110
00100111
00001111
10111100
01011101
11010000
00011100
00000000
11100110
00101101
00001010
11010010
01011011
11001111
01110110
11100111
10101011
00010101
01000010
11100111
01101001

stdout

stderr

js: "/volume/CODE", line 1: missing ; before statement
js: for(;;)java.lang.System c;print(+!(Math.sqrt(8*parseInt(c.in.readLine(),2)+1)%1))
js: .........................^
js: "/volume/CODE", line 1: Compilation produced 1 syntax errors.

strace