>-[-[-<]>>+<]>-[<<++>+>-]<<+<<<-[+>++[++<]>]>-->>[>>>>[-]<<<<[>>+>>+<<<<-]<]<<,<,[>+<-]>[>+>+>>+<<<<-]>>>>--[>.<[-]]>>.>.>+++.>.[<]<<[>>+<<-]>+>[<[-]>[-]]<[->+<]>[>.<[-]]>+.+++.<<<<[>>>+<<<-]>>>>>>>>.<<<<++++++.<-[>>>.<<<[-]]>>>+.+++.
Try it online!
Takes input as two bytes (0 or 1) on stdin, outputs space-separated to stdout without trailing whitespace.
The TIO link has the 11 test case because I couldn't figure out how to type the null character into a web browser, but if you delete the second input character it will do the same thing as the 10 test-case, and if you delete both it will be the same as the 00 test-case.
Here's my annotated version (the two input bytes are b and a, their sum is c):
-[-[-<]>>+<]>- *32* from https://esolangs dot org/wiki/Brainfuck_constants#32
[<<++>+>-] 64 32 *0*
<<+<<< *0* 0 0 65 32
-[+>++[++<]>]>-- *78* 65 32 from https://esolangs dot org/wiki/Brainfuck_constants#78
>>
[>>>>[-]<<<<[>>+>>+<<<<-]<] 0 *0* 0 0 78 65 78 65 32
<<
,<, *b* a 0 0 0 0 78 65 78 65 32
[>+<-]> 0 *b plus a=c* 0 0 0 0 78 65 78 65 32
[>+>+>>+<<<<-]>>>> 0 0 c c 0 *c* 78 65 78 65 32
-- 0 0 c c 0 *c minus 2* 78 65 78 65 32
[>.<[-]]>>.>.>+++.>. 0 0 c c 0 0 78 65 78 *68* 32 (N)AND space print N if c == 2
[<]<<[>>+<<-]>> 0 0 c 0 0 *c* 78 65 78 68 32
<+>[<[-]>[-]]<[->+<]> 0 0 c 0 0 *!c* 78 65 78 68 32
[>.<[-]]>+.+++. 0 0 c 0 0 0 *82* 65 78 68 32 (N)OR print N if c == 0
< <<<[>>>+<<<-]>>> 0 0 0 0 0 *c* 82 65 78 68 32
>>>>>.<<<<++++++.< 0 0 0 0 0 *c* 88 65 78 68 32 space X
-[>>>.<<<[-]] 0 0 0 0 0 *0* 88 65 78 68 32 (N) print N if c != 1
>>>+.+++. 0 0 0 0 0 0 88 65 *82* 68 32
