verilog, 85 bytes

Result

WA

Code [DL]

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

stdin

00110111
01110010
11100011
10101011
01001110
00000011
11110010
11010010
01111011
00000001
11110001
00000100
00010100
11110110
00111101
11000001
00101101
00010011
01101001
00000110
10000100
10011011
10111110
01000010
10001000
00100111
01010100
00010101
00011101
11011011
01111100
11101001
01011011
00001010
11100111
11111101
10100100
00000000
00001111
01110001
00000001
00101100
10011001
01101011
00100100
00011100
10101101
01010001
01111000
00110111

stdout

stderr

/volume/CODE:1: syntax error
/volume/CODE:1: error: malformed statement
/volume/CODE:1: error: Error in while loop condition.
/home/esolang/bin/verilog: line 4: /tmp/code: No such file or directory
rm: cannot remove '/tmp/code': No such file or directory

strace