this presentation explains the nature of digital and binary data. it introduces the number systems such as decimal, binary, octal and hexadecimal. it also explains the addition and subtraction of binary numbers by following their arithmetical rules. explains the different forms of data and forms of processed data.

1. 5/30/2019 1
Samina khan
FDC Risalpur

2. • Chapter 1 Data –Processing Cycle
• Chapter 2 Binary Computing
• Chapter 3 System Software
• Chapter 4 Application Software
• Chapter 5 More on Word
• Chapter 6 More on Spreadsheets
• Chapter 7 Algorithms and Flow charts
• Chapter 8 Introduction to Programming Languages
• Chapter 9 Computer Networks
• Chapter 10 The Internet
• Chapter 11 Communicating through Email
5/30/2019
2

3. CHAPTER 2

4. Objectives
• Explain the nature of digital data and binary data.
• introduce number systems as a set of rules for
representing data using numbers
• explain the decimal, binary, octal, and hexadecimal
number systems
• explain the conversion of decimal numbers into binary
numbers and vice versa
• explain the addition and subtraction of binary numbers
• explain data storage in terms of bits and bytes
5/30/2019 4

5. The Computer: A digital machine
• Computers are electronic machines.
• They understand data in a digital form.
• Computers need to translate data from analog to
digital.

6. Forms of data
• Data is a collection of raw facts and figures
• It is often meaningless
• There are different forms of data
1. Numeric data
2. Alphabetic data
3. Alphanumeric data

7. Digital data
• When data is processed , we get the information
• Computers process data after converting it into a
digital form

8. Binary states
• Bi means two
• In case of current flow we have only two
situations: either current flows or not flow
• These two situations are represented by 0 & 1
• Binary state ON=1 Binary state OFF=0
• The same situation we can observe in memory
unit of a processor.
• Whenever we press a key on keyboard,
electronic signals are sent to the processor.

9. • The processor understand these signals and
process them.
• But human cannot see the electric current.
• This is why we represent these signals as 1s
and 0s
• Data in the form of 1s & 0s is called binary
data.
Input Data Binary Data
10 1010
2 10
12 1100

10. Number Systems
• We use numbers to mean different things.
• We use the digits 0-9 to represent small
numbers like 2 & 5 , and large numbers like 5900
& 99723.
• This system uses 10 digits , it is called decimal
number system.
• There is another number system having 2 digits
0& 1, called binary number system.
Decimal Binary
10 1010

11. Types of number Systems
• There are several number systems but four are
most commonly used. These are:
1. The decimal number system
2. The binary number system
3. The octal number system
4. The hexadecimal number system

12. The decimal number System
• The decimal number system, or Base 10 system
is based on ten digits(0,1,2,3,4,5,6,7,8,9)
• These digits are combined in different ways to
represent different values.
• For Example: (10)10

13. The binary number System
• The binary number system, or Base 2 system is
based on 2 digits(0 &1)
• These digits are combined in different ways to
represent different values.
• For Example: (10)2

14. The octal number System
• The octal number system, or Base 8 system is
based on 8 digits(0,1,2,3,4,5,6 &7)
• These digits are combined in different ways to
represent different values.
• For Example: (12)8

15. The hexadecimal number System
• The hexadecimal number system, or Base 16
system is based on 16 digits(0,1,2,3,4,5,6,7,8,9 &
the letters A,B,C,D,E,F)
• These digits are combined in different ways to
represent different values.
• For Example: (A)16

16. Characters
• Characters are the alphabet keys, number keys and
special keys on the keyboard.
• These are what you see on the keyboard.
• When we press a key on the keyboard, each
character is converted into a unique pattern of 1s &
0s.
• For Example:
Decimal system Binary system
65 01000001
97 01100001

17. Binary coding scheme
• Binary coding schemes are used to convert
characters into binary form and vice versa.
• There are three coding scheme in common use.
1. The ASCII code
2. EBCDIC code
3. Unicode

18. 1. The ASCII code
• ASCII stands for American Standard Code for
Information Interchange

19. 2. The EBCDIC code
• EBCDIC stands for Extended Binary Coded
Decimal Interchange Code.
• It is used in mainframe computers.

20. 3. Unicode
• It was developed in 1990s.
• It developed codes for a large number of
characters including Chinese and Japanese one.
• It is commonly used code to store data on
microcomputers after surpassing ASCII.

21. Conversion of number systems
• We can convert data represented under one
number system into other number system.
• We can convert decimal numbers into binary
number and vice versa.

22. Conversion of decimal numbers into binary
• To convert a decimal number into binary ,we use
the repeated division method.
Number Remainder
2 39
2 19 1
2 9 1
2 4 1
2 2 0
1 0

23. Conversion of binary numbers into decimal
• To convert a binary number into decimal ,we use
the expansion method.
• Convert (100111)2 into decimal
= (1x25)+(0x24) +(0x23) +(1x22) +(1x21) +(1x20)
=(1x32)+(0x16)+(0x8)+(1x4)+(1x2)+(1x1)
=32+0+0+4+2+1
=(39)10

24. Arithmetical operations using binary
numbers
• Binary arithmetic is performed in the same
manner as decimal arithmetic.
• The two basic binary arithmetic operations are:
1. Binary addition
2. Binary subtraction

25. Binary addition
• Binary system is based on only two digits 0 & 1
so its rule of addition is different from decimal
addition.
Operation Result
0+0 0
0+1 1
1+0 1
1+1 0 with 1 carried over to the next higher column

26. Binary addition
0 1 0 1 1 1 0 1
+ 0 0 1 1 0 0 1 0
1 0 0 0 1 1 1 1

27. Binary subtraction
• Binary subtraction is similar to the subtraction of
decimal numbers.
Operation Result
0-0 0
0-1 1 with 1 borrowed from the next position
1-0 1
1-1 0

28. Binary subtraction
1 1
1 01 0 1 1 01 0 1
- 0 0 1 1 0 0 1 0
1 0 0 0 1 0 0 1