js-rhino, 102 bytes

Result

WA

Code [DL]

for(a=new java.util.Scanner(java.lang.System.in);;)print(0==Math.sqrt(parseInt(a.nextLine(),2)*8+1)%1)

stdin

01111000
11010000
11111101
11110100
10001000
00110111
00111101
11110001
11000000
11010010
00000110
00001010
01010011
11011110
10011001
10111110
00001111
10111111
01010010
01101101
11100100
01101001
00100100
11001001
01001110
11101100
10101011
11100111
00000000
10110000
00110111
00000001
01001110
00011100
00010100
11000011
00000011
01110111
01100011
11011010
00010101
11111111
00101101
11110010
10011010
00011000
11111000
01011011
01000010
11011001

stdout

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

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