verilog, 340 bytes

Result

WA

Code [DL]

`define EOF 32'hFFFF_FFFF
`define STDIN 32'h8000_0000
module cat;integer c,i,d;initial begin c=$fgetc(`STDIN);while(c !=`EOF)begin d=0;i=1;while(c==48||c==49)begin d=d*2;d+=c-48;c=$fgetc(`STDIN);end i=1;while(d>0)begin d=d-i;i=i+1;end if(d==0)begin $write("%c\n","1");end else begin $write("%c\n","0");end c=$fgetc(`STDIN);end end endmodule

stdin

01100000
10000011
00100100
00101101
11110010
01011111
11010110
11101110
00000001
00110110
10110001
10101010
01000101
00111000
10101011
00011100
11001110
00001100
00011111
01101001
11111000
10100011
01001110
01001000
11100111
11001001
00010101
00000011
11111101
10011001
00001010
01011011
10001000
10000001
10111110
01011011
01011101
00110111
01010101
00001111
01111000
01000010
01001110
10000101
00000000
11010010
10110010
00010000
00000110
10011111

stdout

stderr

/volume/CODE:3: syntax error
/volume/CODE:3: Syntax in assignment statement l-value.
/home/esolang/bin/verilog: line 4: /tmp/code: No such file or directory
rm: cannot remove '/tmp/code': No such file or directory

strace