What is "binary exponentiation"?

Question

Mathematics

On the Internet I saw only incomprehensible code examples, please explain in words, or with an example.

Answer 1

r := 1;
while (pow > 0) do
if (pow mod 2 = 1) then
begin
r := r * a;
pow := pow-1;
end
else
begin
r := r * r;
pow := pow div 2;
end;
Thus exponentiation takes a little more than ln2(pow) operations, not pow operations.