js-rhino, 103 bytes

Result

AC

Code [DL]

for(c=new java.util.Scanner(java.lang.System.in);;)print(+!(Math.sqrt(8*parseInt(c.nextLine(),2)+1)%1))

stdin

00001001
01001110
00000001
00011010
10111110
11100011
11110011
01111000
01011001
10101100
00001111
00110111
01011011
11000011
00011100
11010010
10101110
01010101
00000000
11010100
10100010
11100111
01001001
00100100
11111101
01101001
00000011
00001010
00010101
01000010
10111111
11000100
00000110
01011101
00010101
01000001
11111100
01111000
00101011
10001000
11100001
11001100
01100011
00100110
10000110
00101101
01110001
01111010
10011001
10101011

stdout

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

stderr

org.mozilla.javascript.WrappedException: Wrapped java.util.NoSuchElementException: No line found
	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.callProp0(OptRuntime.java:85)
	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: No line found
	at java.util.Scanner.nextLine(Scanner.java:1540)
	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