js-rhino, 87 bytes

Result

AC

Code [DL]

for(a=java.util.Scanner(java.lang.System.in);;)print(+!(Math.sqrt(a.nextInt(2)*8+1)%1))

stdin

11010010
00000001
11010110
00100100
00101100
11010010
01011011
11111101
01111000
00001100
11111100
00000000
01010011
10011001
10001000
11011110
01101001
11110010
10101011
11111010
11000100
00111100
10010110
00000011
10111110
01010001
01111000
01110010
00000111
01000010
00011100
00111010
11001111
00110111
00101101
01011100
11000000
00001011
00001111
01000000
01110001
00010101
01101101
11100111
01001110
00001010
01001010
10110001
00000110
11101100

stdout

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

stderr

org.mozilla.javascript.WrappedException: Wrapped java.util.NoSuchElementException
	at org.mozilla.javascript.Context.throwAsScriptRuntimeEx(Context.java:1893)
	at org.mozilla.javascript.MemberBox.invoke(MemberBox.java:148)
	at org.mozilla.javascript.NativeJavaMethod.call(NativeJavaMethod.java:225)
	at org.mozilla.javascript.optimizer.OptRuntime.call1(OptRuntime.java:32)
	at org.mozilla.javascript.gen._volume_CODE_1._c_script_0(Unknown Source)
	at org.mozilla.javascript.gen._volume_CODE_1.call(Unknown Source)
	at org.mozilla.javascript.ContextFactory.doTopCall(ContextFactory.java:393)
	at org.mozilla.javascript.ScriptRuntime.doTopCall(ScriptRuntime.java:3282)
	at org.mozilla.javascript.gen._volume_CODE_1.call(Unknown Source)
	at org.mozilla.javascript.gen._volume_CODE_1.exec(Unknown Source)
	at org.mozilla.javascript.tools.shell.Main.processFileSecure(Main.java:601)
	at org.mozilla.javascript.tools.shell.Main.processFile(Main.java:560)
	at org.mozilla.javascript.tools.shell.Main.processSource(Main.java:531)
	at org.mozilla.javascript.tools.shell.Main.processFiles(Main.java:179)
	at org.mozilla.javascript.tools.shell.Main$IProxy.run(Main.java:100)
	at org.mozilla.javascript.Context.call(Context.java:501)
	at org.mozilla.javascript.ContextFactory.call(ContextFactory.java:503)
	at org.mozilla.javascript.tools.shell.Main.exec(Main.java:161)
	at org.mozilla.javascript.tools.shell.Main.main(Main.java:136)
Caused by: java.util.NoSuchElementException
	at java.util.Scanner.throwFor(Scanner.java:862)
	at java.util.Scanner.next(Scanner.java:1485)
	at java.util.Scanner.nextInt(Scanner.java:2117)
	at sun.reflect.GeneratedMethodAccessor1.invoke(Unknown Source)
	at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
	at java.lang.reflect.Method.invoke(Method.java:498)
	at org.mozilla.javascript.MemberBox.invoke(MemberBox.java:126)
	... 17 more

strace