# Logic

### Overview

Logic gates and logic circuits are the foundation of digital systems. At the most fundamental level complex systems such as flip-flops, bistables, counters and adders are all made from logic gates. This lesson is about logic gates themselves, how to describe systems of logic gates using truth tables and boolean algebra, how to design logic circuits to perform a particular task and how to do all of this with just one type of logic gate. The lesson starts with an introduction to some of the concpets of digital systems.

### Learning Objectives

• Use switches and pull-up or pull-down resistors to provide correct logic level inputs for logic circuits
• Recognise 1 and 0 as logic levels and appreciate these represent voltages in a circuit
• Identify and use NOT gates and 2-input AND, OR, NAND and NOR gates, singly and in combination
• Use data sheets to identify pin connections
• Recall truth tables for each of the 2-input logic gates
• Produce a suitable truth table for a given logic circuit
• Produce a suitable truth table from a given system specification
• Use truth tables to analyse a system of gates
• Design processing systems consisting of logic gates to solve problems
• Design systems from a given truth table
• Simplify logic circuits using NAND gate redundancy
• Use Boolean algebra to represent the output of truth tables or logic gates and use the basic Boolean identities

### Lesson Content

Reading: Introduction to logic circuits. Read about different types of logic circuit and appreciate the difference between combinational and synchronous logic. Consider carefully what is meant by analogue and digital signals and understand that a Logic 1 represents a voltage close to the supply voltage and Logic 0 represents a voltage close to zero volts. Complete the reading in this section by looking at push buttons as inputs and understand that a pull up or pull down resistor is always required.

Reading: All about Logic Gates. Learn the symbol for each logic gate and the associated truth table. Make sure to understand why the logic gates are named as they are so that it is easier to remember their function. Draw out each of the logic gates and the truth table from memory.

Reading: Consider carefully each of the four examples that show how to use intermediate columns to complete a truth table for a circuit containing several different logic gates. Make sure to understand the general principle rather than remembering specific circuit details.

Video (6 min): The Interactive White Board video works through an example of a complex logic circuit built from different logic gates. Watch the video and relate the techniques used to your previous reading.

Reading: Using NAND gates to build any other logic gate has many advantages including making circuits easier to build. Work through the NAND gate equivalent for each different logic gate and try to learn the equivalent circuits. Finally, work through the example circuit where three different logic gates in a circuit are all replaced by their NAND gate equivalents.

Video (11 min): An Interactive White Board video in two parts. The first half looks at each logic gate and considers the NAND gate equivalent. The second half of the video looks at an example circuit which is simplified using NAND gates.

Reading: Complete the work on logic by reading about Boolean algebra. It is important to be able to use Boolean expressions to describe logic circuits and truth tables. The Boolean identities are also useful and help to develop an understanding of the logic gates studied earlier.

Exercises: Complete the exercises about logic circuits.

### Lesson Review

Review your learning by working through the presentations or notes which summarise the website content.

Presentation: Powerpoint download. All the different logic gates and their corresponding truth tables.

Notes: PDF download. Introduction to logic circuits, digital and analogue signals, combinational and sequential logic circuits. Overview of logic gates, their associated truth tables and how to analyse complex logic circuits.

Notes: PDF download. Using NAND gate equivalent circuits to simplify complex logic circuits.

### Self Assessment

Complete either the questions (pdf download) OR the on-line quiz. They are the same questions.

Quiz: Interactive Quiz about basic logic circuits.

Quiz: Interactive Quiz about NAND equivalent circuits and Boolean expressions.

### Self Evaluation

I can:

• Draw the circuit symbols for standard 2-input logic gates
• Recall the truth tables for each of the standard 2-input logic gates
• Understand the meaning of Logic 0 and Logic 1 and appreciate how these relate to voltages in a circuit
• Use data sheets and interpret pin layouts when building logic circuits
• Analyse the operation of a logic circuit using truth tables
• Design a logic system given a system specification
• Build each of the standard 2-input logic gates from NAND gates
• Simplify logic circuits using NAND gate redundancy
• Describe a truth table or logic circuit using Boolean Algebra