goruby, 56 bytes

Result

WA

Code [DL]

loop{a=((8*gets.to_i(2)+1)**(0.5)-1)/2;p(a.to_i==a)?1:0}

stdin

01100111
01100011
00000110
01100101
00001010
00011011
10000010
10111010
00101111
00000011
00110111
01001110
00011110
01101001
01111000
01101010
00101101
11100111
01100100
11101110
00011100
10011001
01000010
00000001
00010101
10111110
00101101
11010010
00011001
00000000
10001000
01011011
10101011
00001110
00001111
10001011
01111110
01001111
10011011
10000011
00010100
11010110
00010110
11111101
10110000
11101001
00101101
01001000
00100100
10001100

stdout

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

stderr

/volume/CODE:1:in `to_i': wrong number of arguments (given 1, expected 0) (ArgumentError)
	from /volume/CODE:1:in `block in <main>'
	from /volume/CODE:1:in `loop'
	from /volume/CODE:1:in `<main>'

strace