simula, 195 bytes

Result

AC

Code [DL]

begin integer a,b,r,i,c;while i<50do begin a:=inint;b:=0;r:=1;while a>0do begin b:=b+r*(a-a//10*10);r:=r*2;a:=a/10;end;c:=sqrt(b*8+1);if c*c=b*8+1then outchar('1')else outchar('0');i:=i+1;end;end

stdin

11000100
11100000
10101011
01100001
00011101
00010010
00000010
00001010
00001101
00000000
00110011
10000010
00110101
10001000
10111110
11100011
11010010
01101001
10011001
00101101
11000111
01011001
10011001
00000011
00010100
01101001
11011010
00000110
00000001
00100011
10101000
00100100
00010101
00000101
01001110
00100010
11100111
00011100
10010010
00001111
01011011
11110100
01000010
11010011
00011011
01111000
11000011
11111101
10111011
00110111

stdout

00100001010001101111001101011001101011011010010101

stderr

Compiling /tmp/code.sim:
gcc -g -O2 -c code.c
code.c: In function ‘main’:
code.c:116:136: warning: implicit declaration of function ‘exit’ [-Wimplicit-function-declaration]
 int main(int __argc, char *__argv[]){__progname= __argv[0];goto __sw;__l0:__rstart(__argc,__argv);goto __start;__l1:__slutt:__rslutt();exit(0);__start:__curent_map=__mapmain;
                                                                                                                                        ^
code.c:116:136: warning: incompatible implicit declaration of built-in function ‘exit’
code.c:116:136: note: include ‘<stdlib.h>’ or provide a declaration of ‘exit’
/tmp/code.sim:1:954: warning: implicit declaration of function ‘__rbe’ [-Wimplicit-function-declaration]
/tmp/code.sim: In function ‘__init’:
/tmp/code.sim:4:19: warning: implicit declaration of function ‘__init_FILE’ [-Wimplicit-function-declaration]
/tmp/code.sim: At top level:
/tmp/code.sim:5:1: warning: return type defaults to ‘int’ [-Wimplicit-int]
/tmp/code.sim:13:1: warning: return type defaults to ‘int’ [-Wimplicit-int]
gcc -g -O2 -o /tmp/code code.o -L/usr/local/lib -lcim

strace