python2, 47 bytes

Result

WA

Code [DL]

while 1:print+((1+8*int(`input()`,2))**.5%2==1)

stdin

01111110
00000000
10101000
11010010
10000101
00001111
00000001
00000000
11101101
10111110
11111101
01101001
00000011
10110000
01011011
00110111
00101101
00000010
10010010
00001010
01010101
00011110
10001111
10001000
00100101
01111000
00001010
01000100
01001110
11001100
10101011
10001001
00000110
10001010
00011100
11001111
10111010
01110111
11100111
00100100
01011111
10011001
11110110
01100001
01000010
00101000
01011010
01010110
11101000
00010101

stdout

stderr

Traceback (most recent call last):
  File "/volume/CODE", line 1, in <module>
    while 1:print+((1+8*int(`input()`,2))**.5%2==1)
ValueError: invalid literal for int() with base 2: '299592'

strace