rdmd, 142 bytes

Result

WA

Code [DL]

import std.stdio;
import std.conv;
void main(){string s;while ((s=readln()).length>3){int i=to!int(split(s)[0],2);writeln((8*i+1)**.5%2==1);}}

stdin

01011011
00001111
10111110
11110101
10011001
00111010
10110000
00110111
10001000
10101011
10100110
00111100
00100100
00110111
10001100
00000000
01000010
01101011
11111101
10110111
11100101
00001101
10000101
00000001
01101001
11011100
00010101
11110000
01010001
01110101
00000111
00010110
11100111
00101101
11010010
01100111
00001010
11110011
10000011
11001000
01011011
00000011
01110001
01111101
00100011
01111000
00011100
01101100
00000110
01001110

stdout

stderr

/volume/CODE.d(3): Error: undefined identifier `split`
/volume/CODE.d(3): Error: can only * a pointer, not a 'double'
Failed: ["dmd", "-v", "-o-", "/volume/CODE.d", "-I/volume"]

strace