c-gcc, 66 bytes

Result

WA

Code [DL]

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

stdin

10001111
00001010
10001101
00101101
00011100
10111110
01101011
01010011
10011001
10001000
11111101
00000001
10100100
11000010
11010010
11101110
00111100
11100111
10011001
00011101
11011010
01111000
10000111
10101011
00000000
00000110
00100010
00111010
00010101
00100100
01000010
10000101
01100111
01001011
00110111
00101100
00110101
01011011
10010100
00000011
11100011
11111001
00110001
01101001
00001111
11110011
01000010
00100001
01111110
01001110

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))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))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))a=sqrt(s=strtol(&s,0,2)*8+1);}
                         ^
/tmp/code.c:1:39: warning: implicit declaration of function ‘sqrt’ [-Wimplicit-function-declaration]
 main(s,a){for(;gets(&s);putw(a*a/s))a=sqrt(s=strtol(&s,0,2)*8+1);}
                                       ^
/tmp/code.c:1:39: warning: incompatible implicit declaration of built-in function ‘sqrt’
/tmp/code.c:1:39: note: include ‘<math.h>’ or provide a declaration of ‘sqrt’
/tmp/code.c:1:46: warning: implicit declaration of function ‘strtol’ [-Wimplicit-function-declaration]
 main(s,a){for(;gets(&s);putw(a*a/s))a=sqrt(s=strtol(&s,0,2)*8+1);}
                                              ^
/tmp/ccVCswlM.o: In function `main':
code.c:(.text.startup+0x5d): 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