Combination of numbers

Question

I am working on online exam application,at the examine Login Question are displayed with 4 or 6 options. Let's take 4 options a b c d, if user select a then the value is 1 if b them value 2 if c then value 4 if d then value 8 if e value 16 if f then value 32:

 a ->  1
 b ->  2
 c ->  4
 d ->  8
 e -> 16
 f -> 32

User may choose multiple options, let suppose user choose a and b then answer is 1 + 2 == 3 three is right answer or user choose a d then 1 + 8 == 9 is the correct answer.

what is the logic to break down 9 into 1, 8 OR 11 into 1, 2, 8 or 35 into 1, 2, 32?

Answer 1

Bitwise operation seems like the way too go.
Since you tagged with Angular, I'll go with a Javascript solution :

function breakdown(input) {
    var values = [1, 2, 4, 8, 16, 32];
    var checked = [];
    for (v of values) {
        if (!!(input & v)) checked.push(v);
    }
    return checked;
}

Test cases:

breakdown(9)
> [1, 8]
breakdown(11)
> [1, 2, 8]
breakdown(35)
> [1, 2, 32]