Chapter 1: Digital Systems and Binary Numbers - Prasad V. Potluri ...

Chapter 1: Digital Systems and Binary Numbers

1.1 Digital Systems 1.2 Binary Numbers 1.3 NumberBase Conversions 1.4 Octal and Hexadecimal Numbers 1.5 Complements of Numbers 1.6 Signed Binary Numbers 1.7 Binary Codes 1.8 Binary Storage and Registers 1.9 Binary Logic

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Digital Systems

? Digital age:

? digital systems play a prominent role in everyday life; used in communication, business transactions, traffic control, spacecraft guidance, medical treatment, weather monitoring, the Internet, and many other commercial, industrial, and scientific enterprises

? Digital system examples:

? mobile phone

? digital camera

? digital versatile disc (DVD), personal digital assistance (PDA), MP3, ...

? digital TV

? most, if not all, of these devices have an embedded specialpurpose digital computer

? Digital computers:

What you will learn in the micro-processor course.

? generality or flexibility

? users can specify and change the program, a sequence of instructions, or the data according to the specific need

? generalpurpose digital computers can perform a variety of informationprocessing tasks that

range over a wide spectrum of applications

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Signal

? Digital systems manipulate discrete elements of information represented in a digital system by physical quantities called signals.

? Voltages and currents are the most common electrical signals. ? The signals in most presentday electronic digital systems use just two discrete values or

binary values ? Binary values are represented abstractly by:

- digit: 0 and 1 A binary digit is called a bit. - logic: False (F) and True (T) - level: Low (L) and High (H) - word: Yes and No - state: On and Off.

? Discrete elements of information are represented with groups of bits called binary codes. For example: 01112 = 710

? Analogtodigital converters perform quantization process on analog (continuous)

signals to form a digital (discrete) signals.

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General-purpose Digital Computer

? The major parts of a computer are a memory unit, a central processing unit (CPU), and input?output units (I/O). [check these in your Computer course]

? Memory unit stores programs as well as input, output, and intermediate data. ? CPU performs arithmetic and dataprocessing operations as specified by the program. ? The program and data prepared by a user are transferred into memory by means of an

input device such as a keyboard. ? An output device, such as a printer, receives the results of the computations, and the

printed results are presented to the user. ? Voice, image, finger touch, gesture, brain wave, ..., also can be used as input or output. ? Communication unit provides interaction with other users through the Internet. ? A digital computer can perform not only arithmetic computations and logical operations

but also can make decisions based on internal and external conditions.

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Hardware Description Language (HDL)

? A digital system is an interconnection of digital modules. ? To understand the operation of each digital module, it is necessary to have a basic

knowledge of digital circuits and their logical function. ? A major trend in digital design methodology is the use of a hardware description

language (HDL) to describe and simulate the functionality of a digital circuit. ? An HDL resembles a programming language and is suitable for describing digital

circuits in textual form, simulating a digital system to verify its operation before hardware is built, and automating the design process in conjunction with logic synthesis tools. ? Ignorance of industry's practices on HDL modeling will lead to cute, but worthless, HDL models that may simulate a phenomenon, but that cannot be synthesized by design tools, or to models that waste silicon area or synthesize to hardware that cannot operate correctly. [take the Digital System Design course for more learning on HDL]

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Decimal Numbers

? Decimal number (base-10 or radix-10)

... a5a4a3a2a1a0.a1a2a3...

Decimal point

digit

aj

Power

105 a5 104 a4 103a3 102 a2 101a1 100 a0 101a1 102 a2 103a3

Example:

7, 329 7 103 3 102 2 101 9 100

? General form of base-r system

an rn an1 rn1 a2 r2 a1 r1 a0 a1 r1 a2 r2 am rm

Coefficient: aj = 0 to r 1

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Base-r Numbers

Example: Base-2, binary

(11010.11)2 (26.75)10 1 24 1 23 0 22 1 21 0 20 1 21 1 22

Example: Base-5

(4021.2)5 4 53 0 52 2 51 1 50 2 51 (511.5)10

Example: Base-8, octal

(127.4)8 1 83 2 82 1 81 7 80 4 81 (87.5)10

Example: Base-16, hexadecimal, (A, B, C, D, E, and F are used for the digits 10 ~ 15, respectively)

(B65 F)16 11163 6 162 5 161 15 160 (46, 687)10

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Binary to Decimal Conversion

Example:

(110101)2 32 16 4 1 (53)10

Special Powers of 2

210 103 (1024) is Kilo, denoted "K" 220 106 (1,048,576) is Mega, denoted "M"

230 109 (1,073,741,824) is Giga, denoted "G" 240 1012 (1,099,511,627,776) is Tera, denoted "T"

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