Numbersystem

8/13/2019 Numbersystem

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Chapter 2

Computer Codes, Programming,

and Operating Systems

Outline

2.1 The Binary and Hexadecimal Number Systems

2.2 Computer Codes

2.3 Computer Programming

2.4 Computer Operating Systems


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2.1 The Binary and Hexadecimal Number Systems

Comparing Binary and Decimal Numbers

Converting from decimal to binary(a)Repeated SubtractionThe highest power of two is first

subtracted from the number. The process is then

repeated, subtracting the next highest power of two

from the remainder.


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(b)Repeated DivisionThe decimal number is repeatedly

divided by two. The remainder, always a 1 or 0,

becomes the binary result.


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Hexadecimal Numbers (From Binary to Hexadecimal)The rule of foursHexadecimal is a popular number

system used with microcomputers. Hex numbers are formed

by grouping the binary digits four at a time, beginning on

the right (the Rule of Fours).

Ex: 11010101 = 165D

From Hexadecimal to Binary

Ex: 1620 = 00100000 2


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From Hexadecimal to Decimal

Ex. 2C16= 2x16+12x1= 4410

From Decimal to Hexadecimal

Ex. 3910 = 39/16 = 2 remainder 7

2/16 = 0 remainder 2

3910 = 2716

Note that, for large decimal numbers, first converting

the decimal number to hexadecimal, and then to binary, may

be easier than converting the number directly to binary.

Data Sizes: byte (8 bits) 8-bit

word (2 bytes) 16-bit

doubleword or dword 32-bit (80386, 80486)

quad word 64-bit (Pentium)


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2.2 Computer Codes

ASCIIThe Standard for TextASCII (American Standard

Code for Information Interchange) was first defined by the

American National Standards Institute in 1968. In this code,

each letter of the alphabet, punctuation mark, and decimal

number is assigned a unique 7-bit code number. With 7 bits,

128 unique symbols can be coded. See Table 2.5.


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Error Detection CodesParityOne of the advantages of ASCII is that it allows

text information to be transmitted between computers over

long distances. This is done by converting the seven parallel

ASCII data bits to bit-by-bit serial form. Using a device

called a modem, the serial data are converted to audio tones,

allowing computer-to-computer communication through the

telephone network.

Example

Transmitter Data Receiver

1)High current or voltage switching in nearby equip.2)Lightning3)Signal distortion due to long cable lengths4)Inductive coupling (cross-talk) between adjacent

conductors

To protect against these errors

a)Parity b) Checksuma) Pari ty


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In many cases, the likelihood of even single bit errors is

very small, and the addition of a single parity bit is very

effective error detection method. Many microcomputer

systems use this technique to protect data bytes fetched from

memory by the processor.

b) ChecksumWhen data is to be transmitted over long

distances via the telephone network, single parity bits are

less effective. This is because the data is subject to burst

noise sources that may persist for several milliseconds,

changing the value of many data bits in the process. This is

the case for a lightning strike.

For this type of noise, data is often protected by

sending a checksum character following the transmission of

a large block of characters. The checksum is computed by

adding the numeric values of all bytes in the block. If the

received checksum does not match the computed checksum

byte, the receiver requests that the entire data block be


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retransmitted.

Checksum can be divided into two types

(1)-checksum(a) 8-bit -checksum

Ex. Graseby 3400 Syringe Pump

Command string structure

()(checksum)(CR)

(hex -checksum)(CR)(LF)

The ASCII codes of the 6 characters is 448

8-bit -checksum = () modulo 256

= (60+83+84+79+80+62)modulo 256

= (448) modulo 256

= 192

= C0h

See Ref. 2, P. 217 Table 14.5


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(b) 7-bit -checksum

A 7-bit -checksum is also commonly used,

and is the remainder after dividing by 128.

ExThe ASCII codes sum is 130

7-bit -checksum = (130) modulo 128

= 2

= 02h

(2) Twos complement checksum (TC-checksum)

TC-checksum = 128(data) modulo 128

The 7-bit TC-checksum is used by a number of medical

devices; two such devices being the Ohmeda 7800 ventilator

and Ohmeda 9000 syringe pump.


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Ex. Ohmeda 7800 ventilator

Command string structure

(:) (command)(parameter)(checksum)(CR)

:VTYC(CR)

The ASCII codes of the 4 characters :VTY is 317

7-bit TC-checksum = 128 - (:VTY) modulo 128

= 128 -(58+86+84+89) modulo 128

= 128 - (317) modulo 128

= 128 - 61

= 67

= C

Twos ComplementThe twos complement code provides a way to

represent positive and negative binary numbers signed

binary numbers

1.If the number is positive, make no changes2.If the number is negative, invert all bits and then add 1.

Ex.6 00000110 +1 = 11111001 +1 = 11111010 = FAH


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Ex. Convert the following signed binary numbers to their

decimal equivalent

(a) 11010001 (b) 01010000 (c) 1000 1111 0101 1101

S(a) 11010001 + 1 = 00101110 + 1 = 00101111 =

2FH-47

Twos Complement ArithmeticThe twos complement coding of negative numbers may

at first seem complicated, but it is actually a very clever

code.

+ 14 = 0000 1110

+ - 20 = 0001 0100 + 1 = 1110 1011 + 1 = + 1110 1100

1111 1010


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OverflowWhenever two signed numbers are added orsubtracted, the possibility exists that the result may be too

large for the number of bits allocated.

Ex. +64 = 0100 0000

+96 = 0110 0000

+160 = 1010 0000

+64 = 0000 0000 0100 0000

+96 = 0000 0000 0110 0000

+160 = 0000 0000 1010 0000

Y2K Problem ! ! ! (http:/y2kbmd.mc.ntu.edu.tw/)

Binary Codes Decimal (BCD)The BCD code provides a way for decimal numbers to

be encoded in a binary form that is easily converted back to

decimal.

Ex. 36710 = 0011 0110 0111 BCD

1001 0101 BCD = 9510

The most common application of BCD is with

seven-segment displays. (See Fig. 2.3)


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2.3 Computer Programming (See Textbook p. 54)Introduction

A computer is usually described by its hardware the

number of bits used by its data and address buses, the

amount of RAM and ROM memory, the type of processor

chip, etc. But to do useful work, it is the software that is

important; that is, the programs that can be run on that

computer.


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There are three different ways of writing these programs

1.Machine language2.Assembly language3.High level language

Machine language:

Object codeThe instruction set of a computer is a list of

the operations that can be performed by the processor. Each

of these instructions has its own unique binary code.

Consider the following 80x86 microprocessor program that

adds two numbers input from a keyboard. (see p. 54)


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Machine language or object code (This is the only code acomputer can execute. However, it is nearly impossible

for a human to work with).

Object code is machine-dependent; that is, object codewritten for an 80x86 processor will only work with

processors in the 80x86 family.

Object code is usually written in hexadecimal form. Theprevious program written in hex becomes:

E4 27 88 C3 E4 27 00 D8 E6 30 F4

Certainly this is more readable than the binary version,

but the function of the program is still hidden.

Assembly language:

When programming a microprocessor, programmers

often use assembly language. This involves using 3-5 letter

abbreviations for the instruction operation codes rather than

the binary or hex object codes. (See Fig. 2.4)


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Source CodeThe assembly language program in Fig. 2.4

is said to be in source-code form.

The development of a modern computer program

actually requires four separate steps

1.Creating the source codeUsing an editor, the source codeof the program is created. For an assembly language

program, this means selecting the appropriate instruction

operation codes to accomplish the task.

2.Compiling the programA compiler program, whichexamines the source-code file created by the editor and

determines the object codes for each instruction in the

program, is then run. When compiling assembly language

programs, the compiler is often referred to as an

assembler.


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3.LinkingAlthough the object code produced by thecompiler is in machine language, it is not in a form that

can be directly executed by the computer. The last step is

to link the object code using a program called the linker.

The linker takes the object file produced by the compile

and combines this with other object files and library

functions to produce an executable program.

The linker produces an executable program. You can now

run the program by simply typing in the name of the

program.

4.DebuggingUsually the program does not work correctlyon the first try, and changes must be made. This involves

reinvoking the editor to modify the source-code file,

recompiling, relinking, and retesting. Locating anf fixing

the source of errors is called debugging.

High level language:

High-level languages are geared more toward the

people writing the programs rather than the computer.


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They are closer to English and save time for programming.

The disadvantageof the Machine and assembly languages

1. Programs are machine dependent and cannot be easilytransferred from one computer system to another

2. Programming is very time consuming to learn. It requiresconsiderable experience to become proficient.

3. Most of the program is occupied with internal detailswhich have very little to do with the actual task to be

accomplished.

4. Programs are difficult to alter due to their complexity.5. It is very easy to introduce errors and crash the computer.The advantageof high-level programming languages

1.Learning to program in a high-level language is easysince the programs are written in a language that the

programmer is accustomed.

2.The programmer does not need to know about theorganization or the internal architecture of the computer.

3.High-level programs require fewer statements. A single


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source statement generates many machine statements.

4.Theoretically, high-level programs are machineindependent, and programs can be run on a great many

different computers.

5.High-level languages have extensive error diagnostics.These help the programmer in locating and correcting

errors in the programs and generally result in a more

friendly environment.

BASIC (Beginners All-Purpose Symbolic Instruction

Code)

Many programmers opt to work in a safer environment.

They choose a high level language that offers an easier to

comprehend syntax together with a built-in safety net that

will prevent their programs from crashing.

BASIC Program

10 INPUT N1, N2

20 PRINT SUN=; N1+N2

30 END


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C Programming

In recent years, C has become the high level language

of choice for most program developers. Also, C is a

structured high level language. (See p. 58 Fig. 2.5)

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