Digital Electronics: Combinational and Sequential Logic, Study notes of Digital Electronics

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Digital Electronics

Part I – Combinational and

Sequential Logic

Dr. I. J. Wassell

Introduction

Course Structure

• 11 Lectures
• Hardware Labs
  • 6 Workshops
  • 7 sessions, each one 3h, alternate weeks
  • Thu. 10.00 or 2.00 start, beginning week 3
  • In Cockroft 4 (New Museum Site)
  • In groups of 2

Objectives

• At the end of the course you should
  • Be able to design and construct simple digital electronic systems
  • Be able to understand and apply Boolean logic and algebra – a core competence in Computer Science
  • Be able to understand and build state machines

Other Points

• This course is a prerequisite for
  • ECAD (Part IB)
  • VLSI Design (Part II)
• Keep up with lab work and get it ticked.
• Have a go at supervision questions plus

any others your supervisor sets.

• Remember to try questions from past

papers

Semiconductors to Computers

• Increasing levels of complexity
  • Transistors built from semiconductors
  • Logic gates built from transistors
  • Logic functions built from gates
  • Flip-flops built from logic
  • Counters and sequencers from flip-flops
  • Microprocessors from sequencers
  • Computers from microprocessors

Combinational Logic

Introduction to Logic Gates

• We will introduce Boolean algebra and

logic gates

• Logic gates are the building blocks of

digital circuits

Logic Variables

• In electronic circuits the two values can

be represented by e.g.,

• High voltage for a 1
• Low voltage for a 0
• Note that since only 2 voltage levels are

used, the circuits have greater immunity

to electrical noise

Uses of Simple Logic

• Example – Heating Boiler
  • If chimney is not blocked and the house is cold and the pilot light is lit, then open the main fuel valve to start boiler. b = chimney blocked c = house is cold p = pilot light lit v = open fuel valve
  • So in terms of a logical (Boolean) expression v = (NOT b ) AND c AND p

Representing Logic Functions

• There are several ways of representing

logic functions:

• Symbols to represent the gates
• Truth tables
• Boolean algebra
• We will now describe commonly used

gates

NOT Gate

Symbol a y

Truth-table a y 0 1 1 0

Boolean y  a

• A NOT gate is also called an ‘inverter’
• y is only TRUE if a is FALSE
• Circle (or ‘bubble’) on the output of a gate

implies that it as an inverting (or

complemented) output

OR Gate

Symbol

a (^) y

Truth-table (^) Boolean y  a  b b

a y 0

1

1

0

b 0 0 1

1 0 1 1 1

• y is TRUE if a is TRUE or b is TRUE (or

both)

• In Boolean algebra OR is represented by

a plus sign 

EXCLUSIVE OR (XOR) Gate

Symbol Truth-table (^) Boolean a y y  a  b 0

0

1

0

b 0 0 1

1 0 1 1 1

• y is TRUE if a is TRUE or b is TRUE (but

not both)

• In Boolean algebra XOR is represented by

an  sign

a (^) y b