rdmd, 130 bytes

Result

WA

Code [DL]

import std.stdio;
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

10110011
01011011
10011110
10001000
00000011
11110011
00000111
10100001
01001010
10111110
10101100
10000111
00010101
11010010
00001111
00001111
11000100
11100001
10101011
10010101
00111100
01011001
00000000
11111101
11110001
00110111
01101001
00001100
01011010
00000001
11000110
01000010
11100111
01011101
00001010
01001101
10011001
01111000
00101101
00100100
01011111
01001110
01100100
10011011
00001111
00011100
00000110
01011100
10001110
11011100

stdout

stderr

/volume/CODE.d(5): Error: template instance to!int template 'to' is not defined
/volume/CODE.d(6): Error: can only * a pointer, not a 'double'
Failed: ["dmd", "-v", "-o-", "/volume/CODE.d", "-I/volume"]

strace