This document discusses number systems and complement notation in computing. It begins by explaining that complement is the negative equivalent of a number. There are two types of complement: r's complement and (r-1)'s complement. Shortcut methods are provided for calculating both types of complement in various number systems like binary, octal, decimal, and hexadecimal. Examples are given to illustrate complement calculations. The document also discusses the use of complement for performing subtraction using addition.

1. Lecture 02
Number Systems
Overview of Programming
CSE115: Computing Concepts

2. 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

3. 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

4. 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

5. 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)

6. Example
• Find the (r-1)’s complement in short cut method.
 (620143)8 Ans: 157634
 (A4D7E)16 Ans: 5B281
 (110100101)2 Ans: 001011010

7. 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.

8. 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

9. 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

10. 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

11. 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)

12. 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

13. Section 2
Introduction to programming

14. Computer Hardware Components
Components of a PC

15. 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

16. 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.

17. 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

18. 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

19. Network Devices
• Connect a computer to the other computers.
• Enable the users to access data or execute
programs remotely.
• Example: modem, Ethernet card

20. 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

21. 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.

22. 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.

23. 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'

24. 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

25. Machine Language
• The only language that the processor actually 'understands‘
• Consists of binary codes: 0 and 1
• Example: 00010101
11010001
01001100
• 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

26. 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

27. 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.

29. 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

30. 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

31. A Simple Program in C
#include <stdio.h>
#include <stdlib.h>
int main()
{
printf("Hello world!n");
return 0;
}

32. 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

33. A Simple Program in C
#include <stdio.h>
#include <stdlib.h>
int main()
{
printf("Hello world!n");
return 0;
}
Beginning of program

34. 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

35. 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

36. Output
Hello world!