there are different number system such as binary, decimal, octal and hexadecimal. binary has 2 digits 0 & 1. decimal has 0 to 9 digits. octal has 0 to 7 digits. and hexadecimal number system has 0 to 9 digits and 10 to 15 are denoted by alphabets. such as A=10, B=11 etc.

1. 7/8/2020 1
Samina khan
Fazaia Degree College Risalpur

2. • Chapter 1 More on Number System
• Chapter 2 Working on Word
• Chapter 3 Working with Spreadsheet
• Chapter 4 Problem solving
• Chapter 5 Introduction to programming
• Chapter 6 Programming in GW-BASIC
• Chapter 7 Data verification & validation
• Chapter 8 Data protection & security
• Chapter 9 Applications of computers
• Chapter 11 The future of Technology
• Chapter 12 Creating webpages
7/8/2020
2

3. CHAPTER 1

4. Lets recall
• Binary & decimal number system.
• Conversion of binary into decimal (Expansion
method)
• Conversion of decimal into binary (Repeated
division)
• Add and subtract two binary numbers
We will learn how to multiply and divide binary numbers

5. 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

6. 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

7. Multiplication of binary numbers
• Multiplying binary numbers is quite simple.
• It only needs to multiply 1s and 0s.
• We also need to remember the rule of addition.
Operation Result
0+0 0
0+1 1
1+0 1
1+1 0 with 1 carried over to the next higher column
Rules of binary addition

8. Example: 1
• Multiply the numbers (111)2and (1011)2
1 0 1 1
x 1 1 1
1 0 1 1
1 0 1 1 x
1 0 1 1 x x
1 0 0 1 1 0 1
Operation Result
0+0 0
0+1 1
1+0 1
1+1 0 with 1 carried over to
the next higher column
1+1+1=11

9. Example: 2
• Multiply the numbers (101)2and (1001)2
Operation Result
0+0 0
0+1 1
1+0 1
1+1 0 with 1 carried over to
the next higher column
x
xx

10. Division of binary numbers
• For division of binary numbers, we need to
remember the rules of binary subtraction.
Rules of binary Subtraction
Operation Result
0-0 0
0-1 1 with 1 borrowed from the next position
1-0 1
1-1 0

11. Example: 1
• Divide (11100)2 by (11)2
Operation Result
0-0 0
0-1 1 with 1 borrowed from
the next position
1-0 1
1-1 0
0011
11√ 11100
–0
10
–0
100
–11
011
–11
XX
0 0 1 1
x 1 1
0 0 1 1
0 1 1 x
1 0 0 1
Lets Check
the answer
now

12. Example: 2
Operation Result
0-0 0
0-1 1 with 1 borrowed from
the next position
1-0 1
1-1 0

13. Conversion of decimal numbers into
octal
• To convert decimal number into binary, we
divide it by 2( Book 7)
• Here we will divide the number by 8.
• We keep dividing the quotient till we get a
quotient less than 8.
• We then record the remainders from bottom
to top to get the answer.

14. Conversion of decimal numbers into
octal
• Example:1 Convert (45)10 into its octal
equivalent.
Number Remainder
8 45
5 5
(45)10 =(55)8

15. Conversion of decimal numbers into
octal
• Example: 2 Convert (228)10 into its octal
equivalent.
Number Remainder
8 228
8 28 4
3 4
(228)10 =(344)8

16. Conversion of decimal numbers into
Hexadecimal
• We can convert decimal into hexadecimal values
using the repeated division method.
• We divide the number by 16.
• We also remember that in the hexadecimal
system values from 10 to 15 are represented by
the letters A,B,C,D,E and F respectively.
Decimal 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Hexadecimal 0 1 2 3 4 5 6 7 8 9 A B C D E F

17. Conversion of decimal numbers into
Hexadecimal
• Here we will divide the number by 16.
• We keep dividing the quotient till we get a
quotient less than 16.
• We then record the remainders from bottom
to top to get the answer.

18. Conversion of decimal numbers into
Hexadecimal
• Example:1 Convert (55)10 into its hexadecimal
equivalent.
Number Remainder
16 55
3 7
(55)10 =(37)16

19. Conversion of decimal numbers into
Hexadecimal
• Example:2 Convert (225)10 into its
hexadecimal equivalent.
Number Remainder
16 225
14 1
(225)10 =(E1)16
Since 14= E

20. Conversion of Octal into decimal
numbers
• Here we will use the expansion method.
• Base will be 8
• Example:1 Convert (74)8 into its decimal
equivalent.
• Solution: (7 x 81) + (4 x 80)
= (7 x 8) + (4 x 1)
= 56 + 4
= 60
(74)8 = (60)10
since 80 =1

21. Conversion of Octal into decimal
numbers
• Example:2 Convert (546)8 into its decimal
equivalent.
• Solution: (5 x 82) +(4 x 81) + (6 x 80)
= (5 x 64)+ (4 x 8) + (6 x 1)
= 320 + 32+6
= 358
(546)8 = (358)10

22. Conversion of hexadecimal into decimal
numbers
• Here we will use the expansion method.
• Base will be 16
• Example: Convert (F8)16 into its decimal
equivalent.
• Solution: (15 x 161) + (8 x 160)
= (15 x 16) + (8 x 1)
= 240 + 8
= 248
(F8)16 = (248)10

23. Quiz
A. Fill in the blanks.
1. According to the rules of binary addition, 1+1=
2. According to the rules of binary subtraction, 10-1=
3. Decimal numbers can be converted into octal by using
the method.
4. Hexadecimal values can be converted into by
using the expansion method.
5. In the hexadecimal system, 14 is represented by the
letter
10
Repeated division
decimal
E
1

24. Quiz
B. State whether the following statement is true or false.
1. In binary addition 1+0= 10 False (1+1=10)
2. The repeated division method is used to convert
decimal numbers into their octal equivalent. True
3. The hexadecimal equivalent of (50) 10 is 36. False (32)
4. Octal numbers are converted into decimal numbers by
the expansion method. True.
5. The octal equivalent of (100) 10 is 64. False (144)