IS 151 Lecture 1 (2015)

IS 151 Digital Circuitry 1
IS 151
Digital Circuitry
Aron Kondoro

Materials, Assessment and Contact
• Book
– Digital Fundamentals, Floyd, T.F
– http://www.amazon.com/Digital-Fundamentals/dp/1292075988/
• Laboratory Software
– Deeds Digital Circuit Simulator
http://www.esng.dibe.unige.it/deeds/
• Assessment:
– 60% Exam
– 40% Coursework
• Test(s), Lab, Exercise(s), Project(s)
• Contact
– My contact is through your Class Representative

Materials, Assessment and Contact
• Additional recommended materials
– Books => Next slide
– Website: http://www.allaboutcircuits.com/vol_4/
– Google

Books
• Gregg, J. R., & John, G. (1998). Ones and zeros: Understanding
Boolean algebra, digital circuits, and the logic of sets (1st ed.). New
York: IEEE Publications,U.S.
• Harris, D. M., & Harris, S. L. (2012). Digital design and computer
architecture (2nd ed.). Waltham, MA: Morgan Kaufmann Publishers
In.
• Maxfield, C. (2008). Bebop to the boolean boogie: An
unconventional guide to electronics (3rd ed.). Oxford: Newnes (an
imprint of Butterworth-Heinemann Ltd ).
• Nisan, N., & Schocken, S. (2008). The elements of computing
systems: Building a modern computer from First principles (history
of computing S.). United States: The MIT Press.
• Petzold, C. (2000). Code: The hidden language of computer
hardware and software (2nd ed.). United States: Microsoft
Press,U.S.
• Scott, C. J. (2009). But how do it know? The basic principles of
computers for everyone. United States: John C Scott.

Introduction
• Digital systems are everywhere i.e. microprocessors
– Laptops, automobiles, mobile phones etc.
• These systems are very complex
– Billions of transistors, many components
• How are they designed? – ABSTRACTION
– Hiding details when not important

Levels of abstraction – Electronic
Computing System

Digital vs. Analog Quantities
• Electronic circuits can be divided into two broad
categories
– 1. Analog Quantities
• Quantities with continuous values (most things that can be measured
quantitatively).
• e.g. air temperature changes over a continuous range of values;
temperature does not change from, say 70 to 71 instantaneously; it
takes on all infinite values in between: see graph
• Other examples: time, pressure, distance and sound

• Diagram: Temperature graph
100
95
90
85
80
75
70
1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
A.M P.M
Temperature (F)
Time of Day

Analog technologies

• Suppose temperature values are taken every hour (sampling), the
graph will look like:

• Diagram: Sampled Temperature graph (page 3)
100
95
90
85
80
75
70
1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
A.M P.M
Temperature (F)
Time of Day

• The sampled values represent the temperature at
discrete points over a 24-hour period.
– i.e. 1,2,3 etc, which are discrete
• The analog quantity (temperature) have been converted
to a form that can be represented in digital form

– 2. Digital Quantities
• Quantities with discrete values
• Data can be processed and transmitted more efficiently and
reliably
• Useful in data storage: e.g. music when converted to digital
can be stored more compactly (e.g.mp3 music)

Digital vs. Analog
• Stairs vs. Ramp

Advantages of Digital
• Immune to noise, distortion
• Can be duplicated easily
– Copying a cd vs copying a tape

Data Representation Basics
• Computing systems are complex devices, dealing with a variety of
information categories
• Computing systems store, present, and modify:
– Text
– Audio
– Images and graphics
– Video
– Etc.

Binary Representation
• Why binary representation (as opposed to decimal or octal, etc..)?
– Cost
• Devices that store and manage digital data are far less expensive and complex for
binary representation.
– Reliability
• More reliable when they have to represent one out of only two possible values.
– Handling
• Electronic signals are easier to maintain if they carry only binary data.

Binary Representation
• One bit can either be 0 or 1.
– Therefore, one bit can represent only two things – 1 and 0
• To represent more than two things, multiple bits are needed
– Two bits can represent four things because there are four combinations of
0 and 1 that can be made from two bits: 00, 01, 10, 11.
• In general, n bits can represent 2n things because there are 2n
combinations of 0 and 1 that can be made from n bits.

Data Formats - How to Interpret Data
• Internal representation must be appropriate
– E.g. Images, sound, and video: have to be digitized
• Images – need detailed description of the data, how color is
represented at each data point
• Sound – need sampling, digitizing
• Video – need sampling and digitizing in space and time (because of
motion)

Codes and Characters
• The problem:
– Representing text strings, such as
Hello, world in a computer
• Each character is coded as a byte (8 bits)
– including blank spaces, commas, full stops
• Most common coding system is ASCII
• To represent alphanumeric characters – 8 bits per character
– 7-bit code : 27 = 128 codes are used (128 characters can be represented)
– 8th bit is unused (or used for a parity bit)
• Two types of codes:
– 95 are “Graphic” codes (visible)
• Alphabetic, numeric and punctuation characters
– 33 are “Control” codes (control features)
• Shift, delete, enter, etc.

Binary Digits
– In digital electronics, there are only two possible states and can
be represented by
• two different voltage levels: HIGH and LOW
• current levels: OPEN and CLOSED
• lamps: ON and OFF
– The two states are called codes, and combinations of the two
are used to represent numbers, symbols, alphabetic characters
and other types of information

Binary Digits
– The two-state number system is called binary, and the two
digits in the binary system are 0 and 1.
• A binary digit is called a bit (binary digit).
– In digital circuits, two voltage levels are used to represent the
two bits
• 1 – represented by a high voltage level (HIGH)
• 0 – represented by a low voltage level (LOW)
– POSITIVE LOGIC – will be used throughout!
– C.f. NEGATIVE logic:, 1 – LOW, 0 – HIGH

Logic Levels
– Logic levels are voltages used to represent a 1 and a 0.
– One voltage level represents a HIGH and one voltage level
represents a LOW.
– Practically, a HIGH or a LOW can be any voltage between a
specified minimum value and a specified maximum.

Logic Levels
• Diagram: Logic level ranges (page 5)
• From the figure, VH(max) and VH(min) represent the maximum and minimum HIGH voltage
values, respectively
• VL(max) and VL(min) represent the maximum and minimum LOW voltage values,
respectively.
• The range of voltages between VL(max) and VH(min) is a range of uncertainty; a voltage in
the range of uncertainty can appear as either a HIGH or a LOW.
HIGH (1)
LOW (0)
Uncertain
VH(max)
VH(min)
VL(max)
VL(min)

Logic Levels
• Examples:
– The high values of a certain digital circuit may range from 2 V
to 5 V and the LOW values from 0 V to 0.8 V.
– If a voltage of 3.5 is applied, the circuit will accept it as a HIGH
(or binary 1); a voltage of 0.5 V will be accepted as a LOW
(binary 0); a voltage of 1 V will be uncertain

Questions
• Differentiate between a digital and an analog quantity
• Give examples of digital and analog systems
• Classify the following into analog (continuous) or digital (discrete)
– (a) Shades of colours in a TV program about landscapes
– (b) TV screen test pattern, white background, black dots only
– (c) Days in a week, Mon, Tues, Wed, Thurs, Fri, Sat, Sun.
– (d) Sine wave
– (e) A musical symphony
– (f) Chairs/seats in a room
– (g) Integers -2, -1, 0, 1, 2, 3,...
– (h) All real numbers

Further reading
• Bebop to the Boolean Boogie – chapter 1
• Digital design and computer architecture – section(s) 1.1,
1.2, 1.3
• Digital fundamentals – section 1.1

• End of Lecture

IS 151 Lecture 1 (2015)

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