goruby, 55 bytes

Result

AC

Code [DL]

loop{a=((8*gets.to_i(2)+1)**0.5-1)/2;p(a.to_i==a ?1:0)}

stdin

01011101
10000100
00110111
00000011
01101001
10001000
10011100
10011000
01001110
10101101
01000001
11111101
11011101
01110111
01001010
00000000
00100100
01111000
01001000
10111001
11000100
10000000
00000110
10101100
10101011
00100100
00101101
11010110
10101111
00011100
00101100
10010001
00010101
00001111
11011011
11100111
00001010
01100001
01011011
10111110
00010100
01000010
11110110
01010001
11010111
00011101
01101001
11010010
00000001
10011001

stdout

0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
1
1
1
1

stderr

/volume/CODE:1:in `to_i': wrong number of arguments (given 1, expected 0) (ArgumentError)
	from /volume/CODE:1:in `block in <main>'
	from /volume/CODE:1:in `loop'
	from /volume/CODE:1:in `<main>'

strace