UPC EETAC Bachelor's Degree in Telecommunications Systems and in Network Engineering EEL


Lecture 5

L2.5: Incomplete functions

The concept of incomplete function (example: water level meter)


[29/2] Minimised equations: SoP or PoS

- Don't-care inputs ("x" or "-")

- Incomplete functions: don't cares outputs

In this page on incomplete functions there is the example project of a tank level meter. In some circuit applications, not all outputs are of interest.

Another circuit that has incomplete logic functions is the BCD_decoder_1digit  represented in Fig. 1 because binary combinations from "1010" to "1111" are invalid, meaning that we are not interested in this outputs, they do not correspond to valid BCD input numbers. An Error output is used to signal the incorrect input situation.

Incomplete functions

Fig. 1. BCD_decoder_1digit truth table and some examples of its canonical equations as an example incomplete logic functions.


Exercise: Plan A: Initial discussion. Obtain the logic functions Error = f( E, D3 D2, D1, D0). Obtain the logic function Y7 =  f( E, D3 D2, D1, D0).

Obtain all the minimised output equations using minilog.

Plan B: Capture the truth table in VHDL and synthesise the circuit for a Cycplone IV FPGA. Print and comment the RTL view.