## Combinational logic design.

### Teaching unit

### Description

Boolean algebra is presented as a basis for formal analysis of digital circuits, and how to proceed to obtain the function that performs a circuit either as a truth table or a logical expression. Then some of the techniques available to simplify logic expressions are explained, such as applying the theorems of Boolean algebra, and through a systematic technique used in practice: the Karnaugh maps. Tymbols used for each logic gate are shown in order to proceed with the implementation and testing by digital circuit simulators equivalent simplified logical expressions. Finally, all the previous knowledge is applied for the design and synthesis of typical combinational circuits such as adders, encoders, multiplexers, etc.

### Objectives

Knowing the different basic logic operations and their corresponding logic gates (AND, OR, NOT, NAND, NOR, XOR, XNOR).

Identify digital Integrated Circuits (IC) needed for a real design, and know how to find the features and operating parameters of the various IC.

Use a digital circuit simulator to validate the correct operation of digital circuits by a schematic design, truth tables and waveforms.

Mastering the different techniques for the simplification of logical functions: Boolean algebra, DeMorgan's theorems and Karnaugh maps, in order to implement more simple logic circuits.

Perform design of combinational circuits from basic components and previusly implemented (hierarchical design) logic gates: adders, comparators, multiplexers, encoders, etc.

### Subjects

#### Lecture topics

- Boolean Algebra, DeMorgan's theorems.
- Logic functions: sum of products / product of sums.
- Simplification of logic functions: Karnaugh maps.
- Logic Gates: Symbols, integrated circuits (IC).
- Basic design of combinational circuits.
- Adders and subtractors.
- Encoders and decoders.
- Multiplexers and demultiplexers.
- Other combinational circuits, comparators, parity generators, etc.

#### Laboratory topics

- Simple combinational circuits.
- Combinational circuits: adders.
- Combinational circuits: encoders.
- Combinational circuits: multiplexers.