php, 58 bytes

Result

WA

Code [DL]

<?php for(;$c=fgets(STDIN);){echo sqrt(8*bindec($c)+1)%1;}

stdin

10001000
00101100
11101000
11000000
01011011
01000010
10001101
00110111
01001110
10011101
00101101
00000000
11100111
00001111
00001010
00110001
01101001
00101110
01001100
00000110
11110001
10011001
10111001
01111000
00101000
00011101
00001101
01110111
11011101
01011011
01000000
00111110
00000001
11010010
10111110
00001010
01110000
00100001
10111101
00010101
11111101
01111011
10101011
10110011
00000011
10111000
00001000
00100100
10001001
00011100

stdout

00000000000000000000000000000000000000000000000000

stderr

strace