# Two-level Circuit Implementation

2017-11-17 17:44:16 zhengxiaowei 110

### Fundamental form

We begin to consider the feasibility of constructing the four-bit adder in fundamental two-level form by looking at the output from the first sum bit, S0. Since the result of the addition will be equally odd and even then the output column for will contain 256 1’s and 256 0’s. Since the truth table has nine inputs, and we need to use all of these as we are considering a fundamental sum of products implementation，then our two-level circuit will need 256 nine-input AND gates plus a 256-input OR gate to perform the summing. This is clearly impractical so we immediately rule out this method.

### Minimised form

The most complex Boolean function in the circuit is the one for Cout since it depends on ail of the nine inputs. The minimised expression for Cout contains over 30 essential prime implicants, which means that this many AND gates plus an OR gate with this number of inputs would be needed for a minimised two-level implementation. Furthermore, some of the input variables (or their complements) must be fed to up to 15 of the 31 essential prime implicants.

Clearly the large number of gates required, the large number of inputs they must possess, and the fact that some signals must feed into many gates, means that this implementation is also impractical, although it is an improvement on the fundamental two-level form. So although the two-level implementation is theoretically the fastest (assuming ideal gates) we see that for this application it is not really practical.