Digital Electronics

Course Introduction,

Number Systems,Conversion between Bases,

andBasic Binary Arithmetic

(Lecture #1)

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Course Introduction

1. Number Systems2. Binary Arithmetic and Binary Codes3. Boolean Algebra4. Basic Logic Gates5. Boolean Expressions6. Karnaugh Maps7. Minimization of Boolean Expressions8. Analysis and Design of Combinational Logic Circuits9. Single-bit and Multi-bit Adder Circuits10. Multiplexers and Demultiplexers11. Decoders and Encoders12. Tri-state devices13. Latches and Flip-Flops14. Registers and Counters15. Analysis and Design of Sequential Logic Circuits16. Memory cells and Memory design

(see syllabus)

Numerical Representation

• Science, Technology, Business all deal with

– Quantities• Measure, monitored, arithmetically manipulated,

recorded……

– Quantities Represented in two ways• Analogue

• Digital

Analog

• Represented by meter movement proportional to the value of the quantity

– Temperature, voltage, current

– Common mercury thermometer

– Automobile speedometer

– Continuous set of values

Digital representation

• Not by continuous variable indicators but by digits (step by step)

– Digital watch

– Digital speedometer

– Digital temperature gauge

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Numbers

52

What does this number represent? What does it mean?

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1011001.101

What does this number represent? Consider the base (or radix) of the number.

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9

Number Systems

Number Systems

R is the radix or base of the number system Must be a positive number R digits in the number system: [0 .. R-1]

Important number systems for digital systems: Base 2 (binary): [0, 1] Base 8 (octal): [0 .. 7] Base 16 (hexadecimal): [0 .. 9, A, B, C, D, E,

F]

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Number Systems

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Positional Notation

D = [a4a

3a

2a

1a

0.a

-1a

-2a

-3]R

D = decimal valuea

i = ith position in the number

R = radix or base of the number

Number Systems

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Power Series Expansion

D = an x R4 + a

n-1 x R3 + … + a

0 x R0

+ a-1

x R-1 + a-2 x R-2 + … a

-m x R-m

D = decimal valuea

i = ith position in the number

R = radix or base of the number

Number Systems

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Base Position in Power Series ExpansionR 4 3 2 1 0 -1 -2 -3

Decimal 1010 10000 1000 100 10 1 0.1000 0.0100 0.0010

Binary 22 16 8 4 2 1 0.5000 0.2500 0.1250

Octal 88 4096 512 64 8 1 0.1250 0.0156 0.0020

Hexadecimal 1616 65536 4096 256 16 1 0.0625 0.0039 0.0002

104 103 102 101 100 10-1 10-2 10-3

24 23 22 21 20 2-1 2-2 2-3

84 83 82 81 80 8-1 8-2 8-3

164 163 162 161 160 16-1 16-2 16-3