c-gcc, 80 bytes

Result

WA

Code [DL]

main(j,s,a){for(;s=strtol(gets(&j),0,2);puts(&a))for(j=a=48;--j;)a+=j*j-j==s*2;}

stdin

10001011
10001000
00101000
11100110
00110111
10101101
01110000
10100111
11111101
01100111
00011100
00001010
10101000
00000111
10101011
10110001
10011001
00011110
11011010
00111001
01000010
01101001
01011011
10111011
11010111
00111100
10100110
00000000
00010101
00001111
11011000
10101100
01111000
00000001
00000110
00101101
11100111
00111010
10010101
00100100
11010010
00110111
11101110
00000011
00000000
01001110
11110111
10111110
00111011
10110000

stdout

stderr

/tmp/code.c:1:1: warning: return type defaults to ‘int’ [-Wimplicit-int]
 main(j,s,a){for(;s=strtol(gets(&j),0,2);puts(&a))for(j=a=48;--j;)a+=j*j-j==s*2;}
 ^
/tmp/code.c: In function ‘main’:
/tmp/code.c:1:1: warning: type of ‘j’ defaults to ‘int’ [-Wimplicit-int]
/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:1:20: warning: implicit declaration of function ‘strtol’ [-Wimplicit-function-declaration]
 main(j,s,a){for(;s=strtol(gets(&j),0,2);puts(&a))for(j=a=48;--j;)a+=j*j-j==s*2;}
                    ^
/tmp/code.c:1:27: warning: implicit declaration of function ‘gets’ [-Wimplicit-function-declaration]
 main(j,s,a){for(;s=strtol(gets(&j),0,2);puts(&a))for(j=a=48;--j;)a+=j*j-j==s*2;}
                           ^
/tmp/code.c:1:1: warning: suggest parentheses around assignment used as truth value [-Wparentheses]
 main(j,s,a){for(;s=strtol(gets(&j),0,2);puts(&a))for(j=a=48;--j;)a+=j*j-j==s*2;}
 ^
/tmp/code.c:1:41: warning: implicit declaration of function ‘puts’ [-Wimplicit-function-declaration]
 main(j,s,a){for(;s=strtol(gets(&j),0,2);puts(&a))for(j=a=48;--j;)a+=j*j-j==s*2;}
                                         ^
/tmp/ccmWeXQK.o: In function `main':
code.c:(.text.startup+0x18): 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