Approach 1: A logic design problem

Multiplying two bits:

	Anything times 0 is 0, so: 0x0 = 0x1 = 1x0 = 0
	1x1 = 1
	Looking at this as a truth table, this is an AND function

Multiplying two 2-bit numbers (A₁A₀ x B₁B₀ = S₃S₂S₁S₀) can be modeled in a truth table and solved as a simple combinational logic problem.

Solution is not easily expanded as bit size grows

Approach 2: Mimic the way we multiply

We can also build a multiplier the way that we do it on paper:

B1    B0 A1    A0 -------- A0B1  A0B0 A1B1  A1B0       --------------------- S3     S2    S1    S0

Each bit-wise multiply is performed with an AND gate. Add the subtotals with Half Adders: