c-gcc, 68 bytes

Result

WA

Code [DL]

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

stdin

00001010
11011101
00100100
11000101
00101011
01000010
10111110
11010010
01011010
00101101
01001011
00000001
10110010
01111000
00110111
00011100
01111000
10001000
01001111
10001001
00001111
11111101
10010101
00010101
00000110
01001110
00000000
01101001
10100100
01100001
11100111
00000011
11101110
11001111
11110001
10100101
01100101
01110010
00101000
11110011
10101011
01011011
11011100
10011001
10111000
00010111
10010000
01101001
11101100
00100001

stdout

stderr

/tmp/code.c:1:1: warning: return type defaults to ‘int’ [-Wimplicit-int]
 main(s,a){for(;gets(&s);putw(a*a/s,1))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);putw(a*a/s,1))a=sqrt(s=strtol(&s,0,2)*8+1);}
                ^
/tmp/code.c:1:25: warning: implicit declaration of function ‘putw’ [-Wimplicit-function-declaration]
 main(s,a){for(;gets(&s);putw(a*a/s,1))a=sqrt(s=strtol(&s,0,2)*8+1);}
                         ^
/tmp/code.c:1:41: warning: implicit declaration of function ‘sqrt’ [-Wimplicit-function-declaration]
 main(s,a){for(;gets(&s);putw(a*a/s,1))a=sqrt(s=strtol(&s,0,2)*8+1);}
                                         ^
/tmp/code.c:1:41: warning: incompatible implicit declaration of built-in function ‘sqrt’
/tmp/code.c:1:41: note: include ‘<math.h>’ or provide a declaration of ‘sqrt’
/tmp/code.c:1:48: warning: implicit declaration of function ‘strtol’ [-Wimplicit-function-declaration]
 main(s,a){for(;gets(&s);putw(a*a/s,1))a=sqrt(s=strtol(&s,0,2)*8+1);}
                                                ^
/tmp/ccd6meWR.o: In function `main':
code.c:(.text.startup+0x62): warning: the `gets' function is dangerous and should not be used.
/home/esolang/bin/c-gcc: line 6:    13 Done                    cat -
        14 Segmentation fault      (core dumped) | /tmp/code

strace