verilog, 85 bytes

Result

WA

Code [DL]

module a;real x;initial repeat(50)$write("%d",$fscanf(1<<31,"%b",x)==(8*x+1)**0.5%2);

stdin

11110001
11001010
11111101
01110010
00000001
01101001
01101110
10111011
01000010
01111000
00110100
00001010
10110100
10110000
11011110
11010010
00100100
10101100
00001111
00110111
01001110
00101101
00000010
00000000
11110101
10001000
10011001
01100010
00000011
00010000
10110011
00000101
11111001
00000110
00011100
01010000
01110110
00010001
10101011
00010110
00001010
01011011
10001000
11101101
01110000
00001110
11100111
00010101
11010001
10111110

stdout

stderr

/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