The units digit in base 2

Let n be a non-zero natural number. Show that if (c₀, …, c_k) is a base-2 expansion of n, then c₀ is the remainder of the Euclidean division of n by 2, and (c₁, …, c_k) is a base-2 expansion of the quotient of that division. (Question II.1 of the assignment.)