is 151 lecture 1 (2015)

IS 151 Digital Circuitry 1

IS 151Digital 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

http://www.allaboutcircuits.com/vol_4/

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


Digital vs. Analog Quantities• 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



Digital vs. Analog Quantities• Suppose temperature values are taken every hour (sampling), the

graph will look like:


Digital vs. Analog Quantities• 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


Digital vs. Analog Quantities• 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


Digital vs. Analog Quantities– 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)

Technology