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
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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 ya

  • 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 yab 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 yab 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