c-gcc, 74 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

00011001
10011001
11110110
11111101
10101011
00001111
00000011
00101110
01000001
00000000
00011100
01101001
11011011
10001000
01101110
11110001
01100011
10100001
00100100
00001010
01000010
00111101
01111011
11001000
11111010
10010011
00101101
01011111
10111110
00110111
01111100
01011011
00011111
01001110
00000001
11100111
10010101
11010101
00101101
01001011
11010010
11111100
01000011
01111000
01101001
10100110
00010101
00000110
10010001
01010000

stdout

01011110011101000011100000101101011100101001101100

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:1:47: 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:1:47: warning: incompatible implicit declaration of built-in function ‘sqrt’
/tmp/code.c:1:47: note: include ‘<math.h>’ or provide a declaration of ‘sqrt’
/tmp/code.c:1:54: 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/cc1PExPv.o: In function `main':
code.c:(.text.startup+0x5c): warning: the `gets' function is dangerous and should not be used.

strace