bash-pure, 187 bytes

Result

WA

Code [DL]

#!bin/sh
for i in `seq 1 50`;do read j;k=`echo "ibase=2; $j"|bc`;s=0;for x in `seq 0 22`;do s=$[$s+$x];if [ $s -eq $k ];then echo -n 1;break;elif [ $x -eq 22 ];then echo -n 0;fi;done;done

stdin

11111101
00110111
11110111
11001111
00000011
01111110
00110101
00000110
11001101
11101000
10111110
01001110
00011001
01101001
10100100
11001110
11010010
10110011
00100001
00100100
00000001
10011010
00010101
10011001
11000111
00100100
10001000
01011011
11011100
10010001
11100111
10010110
10010000
11100000
10011110
00110100
00001111
00101101
01011110
10000011
10101010
00001010
10011001
01000010
00101011
00011100
00000000
01111000
10101011
01110111

stdout

stderr

/bin/bash: warning: setlocale: LC_ALL: cannot change locale (en_US.UTF-8)
/code.bash: line 2: seq: command not found

strace