crystal, 65 bytes

Result

AC

Code [DL]

while a=gets()
b=a.to_i 2
i=0
while b>0
b-=i+=1
end
p b==0?1:0end

stdin

01101001
00100100
01011011
11111101
11001010
00011101
00110111
00011010
10101011
01111110
10011001
10001111
01000111
00000110
01010001
11100000
00010101
10101010
00111101
01000010
01100101
00011100
11010001
01010111
01100011
11010011
01001110
11010110
00111001
10001000
00001010
00000011
01111000
10101011
11110000
01011100
00001111
11100111
10001110
01010100
00000001
00101101
00000110
11010010
00001001
10010001
10111110
00000000
01101011
01001010

stdout

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

stderr

strace