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


Lecture 3

L1.3: Circuit analysis using Boole's algebra (method III)

P1 analysis. Example Circuit_W (a section of Circuit_C)



1.4. Analysis concept map: several methods for analysing simple combinational circuits

Analysis map
Fig. 1. Analysisi map proposing several methods to deduce the circuit's truth table.

1.4.1. Method I: Proteus simulation for truth tables and deducing logic circuits (Lab1_1)

1.4.2. Method II: WolframAlpha engine for calculating truth tables and deducing logic circuits (Lab1_1)

1.4.3. Method III: Pen & paper analysis using Boolean algebra Properties of boolean functions Duality principle, De Morgan's laws Product of sums (PoS) Sum of products (SoP) Any type of equation or non-standard forms

To continue with the example circuit, to solve step 2, it is better to conceive it as a project:

Specifications: Analyse a section of Circuit_C proposed in P1 to be named Circuit_W represented in Fig.2. Find its truth table using method III. This is a rec. on the idea of circuit analysis.

Fig. 2. Circuit_W symbol and internal architecture.

Planning: follow our concept map in Fig. 3

Plan for method III
Fig. 3. Plan for analysis method III.

This is the folder where to save your notes, pictures, scanned diagrams and discussion:


Development. This is Circuit_W solution rec. using the proposed analysis method III.

Equation and algebra
Fig. 3. Developing the project using algebra.

Alternatively, from the circuit equation we obtain a SoP that becomes the sum of minterms adding missing variables in each product using x = x·(x+y').

Testing: This time, testing the validity of the truth table will be simply comparing solutions from other methods.

To complete step 3, repeat and apply all these concepts to Circuit_C proposed in P1

1.4.4. Method IV: Analysis using synthesis and simulation EDA tools (Lab1_2)