In this section we consider the design of a four-bit adder; i.e. a circuit that adds together two four-bit binary numbers. This needs to be a combinational logic circuit and therefore serves as a useful exercise to apply what we have learnt. To recap, we know that any truth table can be implemented using a product of sums or sum of products expression in either a fundamental or minimised(via Boolean algebra or Karnaugh maps for example) form. Using this approach we end up with two-level circuit implementation of AND-OR, OR-AND, NAND-NAND or NOR-NOR. We have not yet considered the practicalities of any circuits we have designed or analysed which is one of the purposes of this section.
We begin by looking again at both the benefits and problems of two-level circuits, before considering this means of implementation for the four-bit adder. We then move on to two other methods of implementation which rely upon a more thorough look at what we want the circuit to do, rather than simply treating it as a combinational logic problem to be approached using fixed rules'.