L2.4 Lecture 5

L2.5: Incomplete functions The concept of incomplete function (example: water level meter)

L3.1 [28/2]

1.5.2.1.2. Minimised equations: SoP or PoS

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

- Incomplete functions: don't cares outputs

For some circuit applications not all outputs are of interest for given input combinations, and thus they may be considered as "don't care" in the truth table.

This Tank_level_meter project exemplifies incomplete output functions.

Another circuit that has incomplete logic functions is the BCD_dec_1digit  represented in Fig. 1 because for this Binary Coded Decimal (BCD) the combinations from "1010" to "1111" are invalid, meaning that we are not interested in circuit outputs when they do not correspond to valid BCD input numbers. An Error output is used to signal (flag) such incorrect input situation.

Fig. 1. The BCD_dec_1digit truth table and examples of its canonical equations as incomplete logic functions. Error signal is a complete function whereas Y(9..0) are incomplete functions.

 

---

Exercise: Initial discussion of the BCD_dec_1digit in Fig. 1.

 Plan A: Obtain the logic function Error = f( E, D3 D2, D1, D0). Obtain the logic function Y7 = f( E, D3 D2, D1, D0). Obtain the minimised output equations using Minilog.

Plan B: Plan a flowchart to capture the truth table in VHDL and synthesise the circuit for a Cyclone IV FPGA. Print and comment the RTL.

 

---