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

10111110
00110111
00000110
10011011
10101110
00001011
01101001
10001110
00010101
00111110
11111101
11110101
11010100
11100111
10101011
11110110
00001111
01000100
01001001
11010010
01101110
11111110
01010000
00000101
10011001
10001000
00001010
01000010
10000111
00110100
01000011
00011100
01001000
00100100
11110010
00000001
00000011
01011001
00101101
00100100
01111011
01111000
00000000
10001000
10001011
01011011
01001110
11101111
11010001
11110100

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