c-gcc, 72 bytes

Result

AC

Code [DL]

main(s,a){for(;gets(&s);putchar(48+a*a/s))a=sqrt(s=strtol(&s,0,2)*8+1);}

stdin

00000000
01110101
00101101
11111011
11011111
11100111
11010010
00000011
00100000
00010101
10111001
00001010
11001010
01100000
00000110
00000100
00000001
00000000
01111000
10010111
01011011
01000010
11100111
00100110
01001000
01010111
00011100
10111110
10101011
01001110
11001011
11100101
00001111
01100100
10101111
10110100
10000000
00100100
10001000
11010000
11001000
11111101
00110111
11011001
01101001
10011100
11101110
00100011
10011001
10100100

stdout

10100111010100101110111000111100100001100110100010

stderr

/tmp/code.c:1:1: warning: return type defaults to ‘int’ [-Wimplicit-int]
 main(s,a){for(;gets(&s);putchar(48+a*a/s))a=sqrt(s=strtol(&s,0,2)*8+1);}
 ^
/tmp/code.c: In function ‘main’:
/tmp/code.c:1:1: warning: type of ‘s’ defaults to ‘int’ [-Wimplicit-int]
/tmp/code.c:1:1: warning: type of ‘a’ defaults to ‘int’ [-Wimplicit-int]
/tmp/code.c:1:16: warning: implicit declaration of function ‘gets’ [-Wimplicit-function-declaration]
 main(s,a){for(;gets(&s);putchar(48+a*a/s))a=sqrt(s=strtol(&s,0,2)*8+1);}
                ^
/tmp/code.c:1:25: warning: implicit declaration of function ‘putchar’ [-Wimplicit-function-declaration]
 main(s,a){for(;gets(&s);putchar(48+a*a/s))a=sqrt(s=strtol(&s,0,2)*8+1);}
                         ^
/tmp/code.c:1:45: warning: implicit declaration of function ‘sqrt’ [-Wimplicit-function-declaration]
 main(s,a){for(;gets(&s);putchar(48+a*a/s))a=sqrt(s=strtol(&s,0,2)*8+1);}
                                             ^
/tmp/code.c:1:45: warning: incompatible implicit declaration of built-in function ‘sqrt’
/tmp/code.c:1:45: note: include ‘<math.h>’ or provide a declaration of ‘sqrt’
/tmp/code.c:1:52: warning: implicit declaration of function ‘strtol’ [-Wimplicit-function-declaration]
 main(s,a){for(;gets(&s);putchar(48+a*a/s))a=sqrt(s=strtol(&s,0,2)*8+1);}
                                                    ^
/tmp/cc237rPv.o: In function `main':
code.c:(.text.startup+0x5c): warning: the `gets' function is dangerous and should not be used.

strace