Double Degree in International Computer Engineering and Management of Business and Technology

Introduction to Computers

The subject tries to initiate the students in the functioning of the computers and it is structured in four parts. The first part´s objective is to study Boolean algebra to understand the representation of the information in the computers. In the second part combinational systems, the binary arithmetic and the computer´s most basic digital circuits are studied. In the third part, the objective is to study the functioning of a computer´s control unity and how the information is memorized. In the four and the last part, the objective is to study small sequential systems that implement the computer´s control units. With this program, the final objective is to initiate the student in the design and analysis of the digital systems, to learn and understand the functioning of a computer, which their basic parts are, to become capable to program a computer with similar language or to solve any type of problems that imply binary solutions around logical systems.
Type Subject
Primer - Obligatoria
Previous Knowledge



Graduates of our program: Introduction to the computers, acquire the knowledge and develop the skills that are indicated below:

1. To have the knowledge of the digital world and of its components as well as the way of designing digital systems from the statement of a problem in real terms, for the practice of system connection, evaluation of the response of the different elements, signs and components. (a)
2. To design and to use systems, components, processes or experiments to obtain the established requisites and to analyze and interpret the obtained results. (b+c)
3. To identify, formulate and solve technological base problems that need a digital system to obtain a solution in a multidisciplinary environment of an individual way or as member of a team. (d+e)
4. To use techniques and system´s designing tools; either as a work process or a methodology to take into account when developing a system from the beginning until it works correctly. The most used tools are the ones of systems simulation. (k)


Part I. Algebra of Boole

1. Systems of numerical representation
1.1 Numerical systems
1.2 Numerical decimal system
1.3 The binary code
1.4 Numerical binary system (binary, octal)
1.5 Numerical hexadecimal system
1.6 Numerical system of base n
1.7 Conversion between the different numerical systems
2 Logical gates and Boolean algebra
2.1 What is a Boolean algebra?
2.2 Booleans constants and Booleans variable
2.3 Logical functions
2.4 True tables
2.5 Logical operations: AND, OR, NOT, NAND, NOR, XOR i NXOR
2.6 Canonical forms
2.7 Boolean´s Theorems
2.8 DeMorgan´s Theorems

Part II. Combinational Systems

1. Logical combinational circuits
1.1 Algebraic simplification
1.2 Karnaugh´s simplification
1.3 Design of logical combinational circuits
2. Functional combinational blocks
2.1 Introduction
2.2 Multiplexers and demultiplexers
2.3 Codifiers and decoders
2.4 Comparators
3. Binary arithmetic
3.1 Introduction
3.2 Binary natural add
3.3 Binary natural sub
3.4 Representation value with sign
3.5 Arithmetical binary add in CA2
3.6 Implementation of an adder
3.7 Extension of the bits in binary numbers with sign
3.8 Natural binary product
3.9 Carry series and parallel

Part III. Elements of memory

1. Elements of memorization
1.1 How is something memorized?
1.2 Synchronization and types
1.3 The bistable R-S
1.4 The bistable D
1.5 The bistable D with asynchronous R-S

2. Registers and memories
2.1 Registers EP/SP.
2.2 Registers EP/SS.
2.3 Registers ES/SP.
2.4 Registers ES/SS.
2.5 Design of E and OE.

3. Counters design
3.1 Introduction to the counters
3.2 Design of synchronous counters
3.3 Design of asynchronous counters
3.4 Capacity of the counters

4. Memories
4.1 Random memories access.
4.1.1 RAM
4.2 Memories of sequential access.
4.2.1 LIFO
4.2.2 FIFO
4.3 Content Memories access.
4.3.1 CAM

Part IV. Introduction to the sequential Systems

1. Sequential systems
1.1 Definition of sequential system
1.2 Concept of transition, stage, diagram or stages machine.
1.3 Model of Moore and Mealy.
1.4 Activation of the variables by flank or by level.

2. Sequential synchronous systems
2.1 Implementation 1: n
2.2 Implementation n: m
2.3 Implementation with records
2.4 Implementation with counters.


1. LSBAD: practice to simulate a circuit and implement it in a cell.
2. LSStarter: practice where a cell to authenticate the LSMaker is design and implemented.


The methodology that we use to teach classes is the magisterial class with the student´s active participation. These magisterial classes are accompanied with practical classes of problems that are included in the class-hours of the subject. These classes are destined to solve problems set by the teachers as an example or by the same students of the theoretical part saw in class before. The proportion of the classes is approximately 50% of theoretical classes and 50% of practical classes.
All the classes have also a process of continue evaluation, where each week the student has a test that indicates the level of the subject´s tracking. This implies that the student has to study in his house the subject studied in class to face the weekly test. Also it includes some problems proposed for house and they´ll comment in class.
The practical part of the subject is carried out every 15 days, in a two-hour session. The practice is thought in order that it is possible to do it during this time and that it does not represent more work for the student.

Practices are carried out during class time. The first session is an explanation about what the student must do, and in the second session students have time to carry out the practice with the presence of a professor that will solve their doubts. After this session, the practice´s result must be handed in to the professor to be checked. In order to make the work easier, students may use the software since it is an environment of free distribution.
All the students have established time with the professor to solve doubts and receive a personalized attention to clarify anything from problems, the theoretical or the practical part.


- The subject has two different parts: the knowledge part and the practices. Their evaluation is independent. To pass the subject it is necessary to approve the theoretical and the practical part separately. The final grade is calculated with the following formula:
Subject´s_grade = 70% - knowledge + 30% - Practices

- The knowledge grade is evaluated form the two half-yearly grades, only if both grades are equal to or higher than 5:

Knowledge = 50% - Semester_1 + 50% - Semester_2

- The semester´s grade is the average of two grades: the exam grade (Ex_Grade) and the continuous evaluation grade (CE_Grade) according to the following formula, only if the exam´s grade is equal to or higher than 3:

Semester_Grade = 60% - Ex_Grade + 40% CE_Grade

- By other hand, the exam grade is calculated with the average of the two grades of the midterm (Midterm_ Ex) and the semester´s final exam grade (Final_Ex) according to the following formula:

Ex_Grade = 70% - Final_Ex + 30% Midterm_Ex

- The semesters will liberate content until the extraordinary exam only if the minimum grade is five (5).

- In June, besides the ordinary exam for the second semester, there is the possibility to take a recovery exam for the first semester for those students who has not passed it before. The first semester grade will be the best grade obtained with the following calculus:
a) 60% of the recovery exam and 40% of the continuous evaluation obtained during the first semester.
b) 100% of the recovery exam.

- Students that don´t pass the ordinary exam in June will have to take the extraordinary exam of the semesters that they had not passed before. The extraordinary exam may be on July or in September. In this case, the final grade of each semester will be the best grade obtained with the following calculus:
a) 60% of the recovery exam and 40% of the continuous evaluation obtained in the correspondent semester.
b) 100% of the recovery exam.

Evaluation Criteria

Objective 1:
- The student must demonstrate that he has acquired the theoretical knowledge on the digital world that introduces the subject [A, C, D, J].
Objective 2:
- The student must demonstrate that he knows to practice not only the knowledge basis, but that he can apply it to solve any kind of non-standard problem in real life[A, D, J, G].
Objective 3:
- The student must demonstrate that he has acquired the aptitude to design systems from a basic statement of the problem. That means he has the capacity to abstract the problem [A].

Additional Material

"Principios Digitales". Tercera Edición. Roger L. Tokheim. Mc Graw-Hill. 1995
"Fundamentos de los Microprocesadores". Segunda Edición. Roger L. Tokheim. Mc Graw-Hill. 1991
"Computer System Architecture". Third Edition. M. Morris Mano. Prentice Hall. 1993
"Computer Organization and Architecture. Principles of Structure and Function". Third Edition. William Stallings. Macmillan. 1993
"Contemporary Logic Design". Randy H. Katz. 1994
"Introducción al diseño lógico digital". John P. Hayes. Addison-Wesley Iberoamericana