crystal, 65 bytes

Result

WA

Code [DL]

while b=gets().to_i 2
i=1
while b>0
b-=i
i+=1
end
p b==0 ?1:0
end

stdin

00001111
01101000
00000001
00100010
00011001
00011111
00110111
01111011
11111101
10011001
10110111
00000110
00011100
00010101
00000110
01111000
00001000
01001110
01011101
00101101
01000010
01010100
10001000
11010010
10101100
01011011
10111101
10101011
00101100
11001111
01110101
00000000
10110000
11100001
00100100
00101101
10111110
10000011
00010011
11101011
00001010
10010101
01010010
00000011
10100011
01101001
11000110
10101111
00001110
11100111

stdout

Error in /volume/CODE:1: undefined method 'to_i' for Nil (compile-time type is (String | Nil)) (did you mean 'to_s'?)

while b=gets().to_i 2
               ^~~~

Rerun with --error-trace to show a complete error trace.

stderr

strace