js-rhino, 102 bytes

Result

WA

Code [DL]

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

stdin

00100100
00000001
00101001
10101011
00100100
10000000
01100011
01101001
00110111
10011001
11110101
10111110
01101100
00001010
01111100
10001100
00000110
00000001
00100110
11001100
11110001
10001111
10001000
11000101
11111101
00011100
10101111
01111010
01001110
00000011
00111000
01110010
11100100
01111111
00100111
00101101
00001111
01011011
01101111
11000110
11100111
00000000
10101100
11010010
00010101
11101101
01000010
10111111
01011110
01111000

stdout

true
true
false
true
true
false
false
true
true
true
false
true
false
true
false
false
true
true
false
false
false
false
true
false
true
true
false
false
true
true
false
false
false
false
false
true
true
true
false
false
true
true
false
true
true
false
true
false
false
true

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