gistfile1.txt

Assumptions: 

I'll assume that I can be passed a negative integer, so I will guard against it.

Cases:

0 -> "0"
1 -> "1"
2 -> "10"
21 -> "10101"
30 -> "11110"

Implementation:

I am going to use while loops to check if the number yields a positive result when subtracted by each of the five binary gate
numbers, starting with 16 and going down to 1. I will then have a switch statement that will add on a number of zeros depending
on how big the number was originally and how many gates it took to reach the number.

Code:

func toBinaryString(num: Int) -> String {
    var binaryString = ""

    guard num > 0 else {return "0"}
    var number = num

        if number - 16 >= 0 {
            number -= 16
            binaryString += "1"
        } else if binaryString.count == 0 {
            binaryString += "0"
    }
        if number - 8 >= 0 {
            number -= 8
            binaryString += "1"
        } else if binaryString.count == 0 || binaryString.count == 1 {
            binaryString += "0"
    }
        if number - 4 >= 0 {
            number -= 4
            binaryString += "1"
        } else if binaryString.count == 0  || binaryString.count == 1 || binaryString.count == 2{
            binaryString += "0"
    }
        if number - 2 >= 0 {
            number -= 2
            binaryString += "1"
        } else if binaryString.count == 0  || binaryString.count == 1 || binaryString.count == 2 || binaryString.count == 3{
            binaryString += "0"
    }
        if number - 1 >= 0 {
            number -= 1
            binaryString += "1"
        } else if binaryString.count == 0  || binaryString.count == 1 || binaryString.count == 2 || binaryString.count == 3 || binaryString.count == 4{
            binaryString += "0"
    }
    while binaryString.first == "0" {
        binaryString.removeFirst()
    }
    
    return binaryString
    
}