What I want to know is the most code efficient way to convert (in swift 2):
I already have a rudimentary and long-winded way of achieving this, but I would like to find a more efficient way.
Both String and Int have initializers which take a radix (base). Combining those, you can achieve all of the conversions:
// Decimal to binary
let d1 = 21
let b1 = String(d1, radix: 2)
print(b1) // "10101"
// Binary to decimal
let b2 = "10110"
let d2 = Int(b2, radix: 2)!
print(d2) // 22
// Decimal to hexadecimal
let d3 = 61
let h1 = String(d3, radix: 16)
print(h1) // "3d"
// Hexadecimal to decimal
let h2 = "a3"
let d4 = Int(h2, radix: 16)!
print(d4) // 163
// Binary to hexadecimal
let b3 = "10101011"
let h3 = String(Int(b3, radix: 2)!, radix: 16)
print(h3) // "ab"
// Hexadecimal to binary
let h4 = "face"
let b4 = String(Int(h4, radix: 16)!, radix: 2)
print(b4) // "1111101011001110"