js-rhino, 106 bytes

Result

AC

Code [DL]

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

stdin

01101001
11010010
11111110
10111111
11001010
01111001
00000001
00001010
00000011
01111000
11111010
11111100
10000101
01000010
01101010
10110001
10111110
11111101
10101011
10001000
00011100
00100101
00110000
00000011
11110010
00000000
01001110
01000001
01111011
01101101
00100100
10011010
00111110
11000100
01011011
10011110
00000110
00101101
00011010
01011011
01101100
11100111
00100110
00001111
10011001
00110111
01010010
01111110
00011110
00010101

stdout

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