IS 151 Lecture 1

IS 151 Digital Circuitry 1

IS 151

Digital Circuitry

Aron Kondoro


Materials, Assessment and Contact

• Book – Digital Fundamentals, Floyd, T.F– Available in the Unit’s library – contact Mr. Mathew Mndeme

• Laboratory Software– Deeds Digital Circuit Simulator – TC labhttp://www.esng.dibe.unige.it/deeds/

• Assessment:– 60% exam– 40% coursework

• Contact– My contact is through your Class Representative


Materials, Assessment and Contact

• Additional recommended materials

– Book: Bebop to the Boolean Boogie, Clive Maxfield

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

– Google

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

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


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 (page 2)

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



• 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)


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


• End of Lecture

IS 151 Lecture 1

Technology