ruby1.8, 580 bytes

Result

AC

Code [DL]

$<.map{|l|p 2[1-(l.to_i(2)*8+1)**0.5%1]}
p 2[1-($_.to_i(2)*8+1)**0.5%1]while gets
p 2[1+($_.to_i(2)*8+1)**0.5%-1]while gets #-
p 2[1--~($_.to_i(2)*8)**0.5%1]while gets

p 2[1--~($_.to_i(2)*8)**0.5%1]while gets


__END__

dw{p 2[1-(1+8*gt.toi(2))**0.5%1]}

$<.map{|l|p (1-(l.to_i(2)*8+1)**0.5).to_i}

$<.map{|l|p (l.to_i(2)*8+1)**0.5%1>0?0:1}
$<.map{|l|p 1[(l.to_i(2)*8+1)**0.5%1*$$]}
$<.map{|l|p 1>>(l.to_i(2)*8+1)**0.5%1*$$}
$<.map{|l|p 0**((l.to_i(2)*8+1)**0.5%1)}

eval"p (1+8*0b%s)**0.5%%1>0?0:1;"*50%$<.to_a
eval"p 0.**0b%s001**0.5%%1;"*50%gets(p).split

stdin

11100111
11000000
00000011
11100011
01111000
01110101
01011011
00011000
00000000
00000110
00011100
11010000
00001010
01010110
11101100
01011101
11101111
10011001
10101111
00100110
10100101
11111101
00100100
00111100
10111110
00101101
10001000
01011110
00010001
01011100
00110111
01000010
00000000
11010010
00101111
01001110
00001111
11000011
01101001
10001010
01111101
11110001
01000110
00000001
10011001
00010101
10101011
10001101
11111010
00001011

stdout

1
0
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0

stderr

strace