verilog, 73 bytes

Result

WA

Code [DL]

module c;real d;while($fscanf(1<<31,"%b",d))$write($sqrt(d*8+1)%2==1);end

stdin

11111101
01001000
00011010
01000101
11100111
00101101
01001110
11000111
11100111
10101011
00000011
11111100
01101111
11101101
00111001
10001000
10110111
11000011
00011100
10110100
01000000
00010101
00100100
00000100
10000111
01000011
00000000
10111110
11010010
01101001
01011011
01101010
00010010
11101100
00100010
00000110
10110101
00101111
11100100
01111000
00000001
11101011
00001111
01000010
00110111
00001010
00000011
11001000
10011001
10111011

stdout

stderr

/volume/CODE:1: syntax error
/volume/CODE:1: error: invalid module item.
/volume/CODE:1: syntax error
I give up.
/home/esolang/bin/verilog: line 4: /tmp/code: No such file or directory
rm: cannot remove '/tmp/code': No such file or directory

strace