vim, 122 bytes

Result

AC

Code [DL]

00000000  71 7a 22 61 78 22 62 78  22 63 78 22 64 78 22 65  |qz"ax"bx"cx"dx"e|
00000010  78 22 66 78 22 67 78 22  68 73 12 3d 40 61 2a 31  |x"fx"gx"hs.=@a*1|
00000020  32 38 2b 40 62 2a 36 34  2b 40 63 2a 33 32 2b 40  |28+@b*64+@c*32+@|
00000030  64 2a 31 36 2b 40 65 2a  38 2b 40 66 2a 34 2b 40  |d*16+@e*8+@f*4+@|
00000040  67 2a 32 2b 40 68 0a 1b  63 63 12 3d 70 6f 77 28  |g*[email protected].=pow(|
00000050  66 6c 6f 6f 72 28 73 71  72 74 28 40 40 2a 38 2b  |floor(sqrt(@@*8+|
00000060  31 29 29 2c 32 29 3d 3d  40 40 2a 38 2b 31 0a 1b  |1)),2)==@@*8+1..|
00000070  6a 5e 71 34 39 40 7a 5a  5a 0a                    |j^q49@zZZ.|
0000007a

Disassembly

qz"ax"bx"cx"dx"ex"fx"gx"hs<C-R>=@a*128+@b*64+@c*32+@d*16+@e*8+@f*4+@g*2+@h<NL><Esc>cc<C-R>=pow(floor(sqrt(@@*8+1)),2)==@@*8+1<NL><Esc>j^q49@zZZ<NL>

stdin

01001001
10011001
00110111
10111000
11111111
10101101
00001001
10111110
01100101
01001110
11010101
01111000
01010111
10001000
10110000
00011100
00111011
00001111
11010010
00100000
10110011
10101011
01001110
11011110
00000000
01101101
01000111
01000001
01000010
00111001
11100111
00000110
00001010
11111101
10101111
00101101
00100100
00000001
01111110
11111101
01101001
01100011
10011111
00010101
10011010
01011011
10111001
00000011
10111011
00001100

stdout

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

stderr

strace