﻿ Digital Circuits and Systems - Circuits i Sistemes Digitals (CSD) - EETAC - UPC

## Week 1: Analysis of simple combinational circuits. Boole's Algebra

 [12/09] Guided activities #1 [P1] Course presentation and basic logic gates AND, OR, NOT, XOR, NOR, NAND, NXOR

This is the course presentation.

The concept of a logic gate represented in two complementary ways (schematic/symbol/logic diagram and logic equation) and its truth table to describe its specifications or how does it works. Class notes (1)

 [16/09] Laboratory #1 [P1]  Circuit analisys: determine the truth table Method I: Circuit schematics. Electronic circuits simulation using Proteus Method II: Circuit equation. WolframAlpha numerical engine

P1: Section A - method #1: Plan, develop and test: Proteus simulation and virtual lab

In the lab, accordingly to our plan, we'll run the method (I) for obtaining the Circuit_W truth table W = f (D1, D0, A, B): a Proteus simulation. Be aware to place the project file here (virtual desktop, SMB drive):

L:\CSD\P1\Proteus\Circuit_W\Circuit_W.pdsprj

Some lab notes (1) on how to proceed with Proteus to deduce the truth table. For instance, Circuit_W.pdsprj is the circuit copied and adapted from the Proteus tutorial.

P1: Section A - method #2: Plan, develop and test - WolframAlpha numerical engine

This is another way to deduce a circuits' truth table, let's use a web-based calculator (or computer engine) like WolframAlpha. This is a text file containing some equations from the Circuit _W to copy and paste into WolframAlpha. Lab notes (1). Remember that is important to reorder, if necessary, the columns of the truth table W = f (D1, D0, A, B).

Evidently, in the end, the two methods experimented (and the other two refered in the plan to be solved the next sessions) will produce the same truth table. Thus, you can assess the project yourself.

 [17/09] Lecture #1 [P1] Circuit analysis, gates and CSD project design flow Circuit analysis using Boole's Algebra (method #3) How to organise a project in CSD?  Logic gates and technology (voltage levels)

P1: Section A - method #3: Plan, develop and test - Boole's algebra and equations

As we did in the lab, let's start with the analysis of a section of the Circuit_C proposed in P1 to be named Circuit_W.

Let's discuss the general plan that will include up to 4 different proceedings to analyse the circuit.  So, the pen-and-paper analysis, method #3 of the Circuit_W gives you firstly the PoS (equation 1) and then the truth table by means of the expression of the product of maxterms. Class notes: (1), (2) and other ideas on maxterns and minterns (3)

Alternatively, if you develop further the circuits' equation you'll get a SoP which becomes the sum of minterns once you've added the missing variables in each product using x = x(y+y') = x·y + x·y'

Do it again for the Circuit_C , Circuit K  or aother similar gate-based circuits. The more you practise the better. Other examples are here.

How to organise each project or problem in CSD? Each project section must be in a different sheet of paper (4 sheets of paper at least).

 1. Specifications What do I have to do? Theory and other tutorials. 2. Planning Graphics, schematics, circuits, models, concept maps, general ideas, process flowchart, bullet lists, etc. 3. Development Commented computer source files, computer results, graphics, pictures, timing diagrams, truth tables, etc. whatever necessary to demonstrate that you solved the problem following your plan. 4. Test Verifications, comparisons, simulator and computer results, explanations and discussions to demonstrate that your project works as expected.

These are examples (1), (2) on how solutions can the organised and reported following this template of 4 sections. Furthermore, because most of the analysis and designs will require computer tools and applications, you must create a folder for storing each project files in our virtual desktop and SMB drive. Print and comment the most meaningfull files and graphics.

Further discussion on logic voltages (VoH, VoL, ViH, ViL, Vcc, GND), technology 74LS (for instance the chip 74LS04) or the CMOS 4069. Noise Margin High (NMH) and Noise Margin Low (NML), output current, etc.

This is another version of the Circuit_W where you can add to the digital electronic circuit Chip1 some buttons, switches, LED's and even relays and motors. Play with the circuit and pay attention to the real voltages that represent '0' and '1' signals.

Additional concepts and tutorials to study and practise

Work load and projects solved: 1 week of class + 5 hours more out of class of study --> 12 sheets of paper (at least). 1. Specify, 2. Plan, 3. Develop, and 4. Check different methods for analysing a given circuit.

This is the list of proposed projects in this P1. So, be professional, do the work in a weekly basis and do not hesitate to ask us in class or by email as many questions as necessary to advance proficiently.