Question

I’ve been given a tip the following code will work, and it does, however I am using it in a little research project and need to thoroughly understand what exactly is the principle behind it.

for i:=0 to (PNum-1) do begin
for j:=0 to (SMax-1) do begin
write(f, ((i shr j) and 1));
end;
writeln(f);
end;

Basically, it generates all PNum variations of SMax-symbol long string containing 0 and 1. My question is, what does ((i shr j) and 1) (shr being right bit shift in Pascal) do?

Thank you in advance.

Answer 1

The expression

((i shr j) and 1)

extracts the j-th bit from the binary representation of `i´ (bits counting from zero from the right).

Example:

i = 23; j = 3;

bin[23] = 10111    
bin[23 shr 3] = 10111 shr 3 = 10
bin[23 shr 3] and 1 = 10 and 1 = 0

Note: the algorithm builds all combinations of [0,1] if PNum = 2^SMax and not all permutations.