Lecture 02Number SystemsOverview of Programming

CSE115: Computing Concepts

Complement

• Complement is the negative equivalent of a number.

• If we have a number N then complement of N will give us another number which is equivalent to –N

• So if complement of N is M, then we can say M = -N

• So complement of M = -M = -(-N) = N

• So complement of complement gives the original number

Types of Complement• For a number of base r, two types of complements can be found

1. r’s complement

2. (r-1)’s complement

• Definition:

If N is a number of base r having n digits then

o r’s complement of N = rn – N and

o (r-1)’s complement of N = rn-N-1

Example• Suppose N = (3675)10

• So we can find two complements of this number. The 10’s complement and the 9’s complement. Here n = 4

• 10’s complement of (3675) = 104 - 3675

= 6325

• 9’s complement of (3675) = 104 - 3675 -1

= 6324

Short cut way to find (r-1)’s complement

• In the previous example we see that 9’s complement of 3675 is 6324. We can get the result by subtracting each digit from 9.

• Similarly for other base, the (r-1)’s complement can be found by subtracting each digit from r-1 (the highest digit in that system).

• For binary 1’s complement is even more easy. Just change 1 to 0 and 0 to 1. (Because 1-1=0 and 1-0=1)

Example

• Find the (r-1)’s complement in short cut method.

(620143)8 Ans: 157634

(A4D7E)16 Ans: 5B281

(110100101)2 Ans: 001011010

Short cut way to find r’s complement

• From the definition we can say, r’s complement of (N) = (r-1)’s complement +1

• So, we can first find the (r-1)’s complement in short cut way then add 1 to get the r’s complement.

• Example: r’s complement of (620143)8 =157634 + 1

= 157635

This method is a two step process. But we can find it in a one step process also.

Short cut way to find r’s complement

• One step process:

Start from rightmost digit to left.

Initial zeros will remain unchanged

Rightmost non-zero digit will be subtracted from r

Rest of the digits will be subtracted from r-1

• Example:

Find the 10’s complement of (529400)10

Rightmost 2 zeros will not change, 4 will be subtracted from 10 and rest of the digits 529 will be subtracted from 9

So the result is 470600

Example

• Find the r’s complement in short cut method.

• (8210)10 Ans: 1790

• (61352)10 Ans: 38648

• (6201430)8 Ans: 1576350

• (A4D7E0)16 Ans: 5B2820

Example for binary

• For binary: start from rightmost bit

• Up to first 1 – no change.

• For rest of the bits toggle (Change 1 to 0 and 0 to 1)

(11010010100)2 Ans: 00101101100

(01101001011)2 Ans: 10010110101

(10000000)2 Ans: 10000000

Use of Complement

• Complement is used to perform subtraction using addition

• Mathematically A-B = A + (-B)

• So we can get the result of A-B by adding complement of B with A.

• So A-B = A + Complement of (B)

Addition and Subtraction

◦ Two's complement addition follows the same rules as binary addition.

◦ Two's complement subtraction is the binary addition of the minuend to the 2's complement of the subtrahend (adding a negative number is the same as subtracting a positive one).

5 + (-3) = 2 0000 0101 = +5

+ 1111 1101 = -3

0000 0010 = +2

7 - 12 = (-5) 0000 0111 = +7

+ 1111 0100 = -12

1111 1011 = -5

Section 2Introduction to programming

Computer Hardware Components

Components of a PC

Input / Output Devices

• Input Devices• Accepts information from the user and

transforms it to digital codes that the computer can process

• Example: keyboard, mouse, scanner

•Output Devices• An interface by which the computer conveys

the output to the user• Example: monitor, printer

Main Memory• A semiconductor device which stores the information

necessary for a program to run.• 2 types

• ROM (Read Only Memory)• Contains information that is necessary for the computer to boot up

• The information stays there permanently even when the computer is turned off.

• RAM (Random Access Memory)• Contains instruction or data needed for a program to run

• Gets erased when the computer is turned off.

Central Processing Unit (CPU)• Does most of the work in executing a program

• The CPU inside a PC is usually the microprocessor

• 3 main parts:• Control Unit

• Fetch instructions from main memory and put them in the instruction register

• ALU (Arithmetic Logic Unit)• Execute arithmetic operations

• Registers• Temporarily store instructions or data fetched from memory

Storage Devices

• A magnetic device used to store a large amount of information.

• Store the software components or data needed for the computer to execute its tasks.

• Can be “read only” or “writable”.

• Example: Hard drive, CD ROM, floppy disks

Network Devices

• Connect a computer to the other computers.

• Enable the users to access data or execute programs remotely.

• Example: modem, Ethernet card

Natural language

• Our everyday-language; spoken and written• Not 100% needed to understand:

• “Do you want to buy this computer ?” remains comprehensible

• Depends on circumstances; the context:• “Do you like one ?” doesn't make sense on its own. It needs a situation

around it:• someone holding a bouquet of flowers: you might take one• someone pointing to an expensive car: your opinion is asked• someone 'offers' you an oily cloth to sneeze: you don't take it

Semantics and Syntax

• Semantics – the meaning of the language within a given context

• Syntax - Syntax are the rules to join words

together in forming a correct expression or phrase.

• In natural languages it is often possible to assemble a sentence in more than one correct ways.

What is Programming?• Programming is instructing a computer to do something for you with the help of

a programming language

• The two roles of a programming language:

• Technical: It instructs the computer to perform tasks.

• Conceptual: It is a framework within which we organize our ideas about things and processes.

• In programming, we deal with two kind of things:

• Data - representing 'objects' we want to manipulate

• Procedures -'descriptions' or 'rules' that define how to manipulate data.

Programming Language

• A programming language contains instructions for the computer to perform a specific action or a specific task:• 'Calculate the sum of the numbers from 1 to 10‘

• 'Print “I like programming”‘

• 'Output the current time'

Programming Language• Can be classified into as a special-purpose and general-purpose

programming languages.

• Special-purpose : is design for a particular type of application• Structured Query Language (SQL)

• General-purpose : can be used to obtain solutions for many types of problems• Machine Languages

• Assembly Languages

• High-Level Languages

Machine Language• The only language that the processor actually 'understands‘

• Consists of binary codes: 0 and 1• Example: 00010101

1101000101001100

• Each of the lines above corresponds to a specific task to be done by the processor.

• Programming in machine code is difficult and slow since it is difficult to memorize all the instructions.

• Mistakes can happen very easily.

• Processor and Architecture dependent

Assembly Language• Enables machine code to be represented in words and numbers.

• Example of a program in assembler language:

LOAD A, 9999

LOAD B, 8282

SUB B

MOV C, A

LOAD C, #0002

DIV A, C

STORE A, 7002

• Easier to understand and memorize (called Mnemonics), compared to machine code but still quite difficult to use.

• Processor and Architecture dependent

High-Level Language• Use more English words. They try to resemble English sentences.

Therefore, it is easier to program in these languages.

• The programming structure is problem oriented - does not need to know how the computer actually executes the instructions.

• Processor independent - the same code can be run on different processors.

• Examples: Basic, Fortran, Pascal, Cobol, C, C++, Java

• A high level language needs to be analyzed by the compiler and then compiled into machine code so that it can be executed by the processor.

C Programming Language

Why 'C' ?

• Because based on 'B'; developed at Bell Laboratories

• Developed by Dennis Ritchie at Bell Laboratories in the 1960s

• In cooperation with Ken Thomson it was used for Unix systems

• The C Language was only vaguely defined, not standardized, so that almost everyone had his own perception of it, to such an extend that an urgent need for a standard code was creeping up

C Programming Language

• In 1983, the American National Standards Institute (ANSI) set up X3J11, a Technical Committee to draft a proposal for the ANSI standard, which was approved in 1989 and referred to as the ANSI/ISO 9899 : 1990 or simply the ANSI C, which is now the global standard for C.

• This standard was updated in 1999; but there is no compiler yet

A Simple Program in C

#include <stdio.h>

#include <stdlib.h>

int main()

{

printf("Hello world!\n");

return 0;

}

A Simple Program in C

#include <stdio.h>

#include <stdlib.h>

int main()

{

printf("Hello world!\n");

return 0;

}

standard Library, input-output, header-file

A Simple Program in C

#include <stdio.h>

#include <stdlib.h>

int main()

{

printf("Hello world!\n");

return 0;

}

Beginning of program

A Simple Program in C

#include <stdio.h>

#include <stdlib.h>

int main()

{

printf("Hello world!\n");

return 0;

}

End of Segment

Start of Segment

A Simple Program in C

#include <stdio.h>

#include <stdlib.h>

int main()

{

printf("Hello world!\n");

return 0;

}

Function for printing text

End of statement

Insert a new line

Output

Hello world!