Numbering system
Download
1 / 29

Numbering System - PowerPoint PPT Presentation


  • 102 Views
  • Uploaded on

Numbering System. Base Conversion. Number systems. Decimal – 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Binary – 0, 1 Octal – 0, 1, 2, 3, 4, 5, 6, 7 Hexadecimal system – 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. Why different number systems?.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Numbering System' - alan-brooks


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Numbering system

Numbering System

Base Conversion


Number systems
Number systems

  • Decimal – 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

  • Binary – 0, 1

  • Octal – 0, 1, 2, 3, 4, 5, 6, 7

  • Hexadecimal system – 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F


Why different number systems
Why different number systems?

  • Binary number result in quite a long string of 0s and 1s

  • Easier for the computer to interpret input from the user


Base conversion
Base Conversion

  • In daily life, we use decimal (base 10) number system

  • Computer can only read in 0 and 1

    • Number system being used inside a computer is binary (base 2)

    • Octal (base 8) and hexadecimal (base 16) are used in programming for convenience


Base conversion1
Base Conversion

  • Conversion

    • Binary number,

    • Octal number,

    • Hexadecimal number, and

    • Decimal number.



Base conversion3
Base Conversion

For example:

62 = 111110 = 76 = 3E

decimal binary octal hexadecimal

1 For Decimal:

62 = 6x101 + 2x100

2 For Binary:

111110 = 1x25 + 1x24 + 1x23 + 1x22 + 1x21 + 0x20

3 For Octal:

76 = 7x81+ 6x80

4 For Hexadecimal:

3E = 3x161 + 14x160

  • Since for hexadecimal system, each digit contains number from 1 to 15, thus we use A, B, C, D, E and F to represent 10, 11, 12, 13, 14 and 15.


Binary and decimal system
Binary and decimal system

  • Binary to decimal

    • X . 27 + X . 26+ X . 25+ X . 24 + X . 23+ X . 22+ X . 21 + X . 20

  • Decimal to binary

    • Keep dividing the number by two and keep track of the remainders.

    • Arrange the remainders (0 or 1) from the least significant (right) to most significant (left) digits


Octal and hexadecimal system
Octal and Hexadecimal system

  • Binary to Octal (8 = 23)

    • Every 3 binary digit equivalent to one octal digit

  • Binary to Hexadecimal (16 = 24)

    • Every 4 binary digit equivalent to one hexadecimal digit

  • Octal to binary

    • Every one octal digit equivalent to 3 binary digit

  • Hexadecimal to binary

    • Every one hexadecimal digit equivalent to 4 binary digits


Base conversion4
Base Conversion

  • How to convert the decimal number to other number system

    • e.g. convert 1810 in binary form

      2 |18 ----0

      2 |09 ----1

      2 |04 ----0

      2 |02 ----0

      1

    • 1810 = 100102


Base conversion5
Base Conversion

  • e.g. convert 1810 in octal form

  • Since for octal form, one digit is equal to 3 digits in binary number, we can change binary number to octal number easily.

    e.g. 10010 = 010010

    2 2

    Thus, 100102 = 228


Base conversion6
Base Conversion

  • e.g. convert 1810 in hexadecimal form

  • Similarly, for hexadecimal form, one digit is equal to 4 digits in binary number.

    e.g. 10010 = 00010010

    1 2

    Thus, 100102 = 1216


Numbering system1

Numbering System

Addition & Subtraction


Decimal addition
Decimal Addition

  • What is going on?

  • 1 1 1 (carry)

  • 3 7 5 8

  • + 4 6 5 7

    • 14 11 15

    • 10 10 10 (subtract the base)

    • 8 4 1 5

111

3758

+ 4657

8415


Binary addition
Binary Addition

Rules.

  • 0 + 0 = 0

  • 0 + 1 = 1

  • 1 + 0 = 1

  • 1 + 1 = 2 = 102 = 0 with 1 to carry

  • 1 + 1 + 1 = 3 = 112 = 1 with 1 to carry


Binary addition1
Binary Addition

  • Verification

    • 5510

    • + 2810

    • 8310

    • 64 32 16 8 4 2 1

    • 1 0 1 0 0 1 1

  • = 64 + 16 + 2 +1

  • = 8310

1 1 1 1

1 1 0 1 1 1

+ 0 1 1 1 0 0

2 3 2 2

- 2 2 2 2

1 0 1 0 0 1 1


Binary addition2
Binary Addition

ex Verification

1 0 0 1 1 1

+ 0 1 0 1 1 0 + ___

___________

128 64 32 16 8 4 2 1

=

=


Octal addition
Octal Addition

1 1

6 4 3 78

+ 2 5 1 08

9 9

- 8 8 (subtract Base (8))

1 1 1 4 78


Octal addition1
Octal Addition

ex

3 5 3 68

+ 2 4 5 78

- (subtract Base (8))


Hexadecimal addition
Hexadecimal Addition

1 1

7 C 3 916

+ 3 7 F 216

20 18 11

- 16 16 (subtract Base (16))

B 4 2 B16


Hexadecimal addition1
Hexadecimal Addition

8 A D 416

+ 5 D 616

- (subtract Base (16))

16


Decimal subtraction
Decimal Subtraction

7 13 10

8 4 1 15

- 4 6 5 7

3 7 5 8

  • How it was done?

  • ( add the base 10 when borrowing)

  • 1010

  • 73010

  • 8 41 5131015

    • - 4 6 5 7

    • 3 7 5 8


Binary subtraction
Binary Subtraction

  • Verification

    • 8310

    • - 2810

    • 5510

    • 64 32 16 8 4 2 1

    • 1 1 0 1 1 1

  • = 32 + 16 + + 4 + 2 +1

  • = 5510

1 2 1

02 0 2 2

1 0 1 0 0 1 1

- 0 1 1 1 0 0

1 1 0 1 1 1


Binary subtraction1
Binary Subtraction

ex Verification

1 0 0 1 1 1

- 0 1 0 1 1 0 - ___

___________

128 64 32 16 8 4 2 1

=

=


Octal subtraction
Octal Subtraction

8

0 0 8

1 11 4 78

89

- 6 4 3 78

2 5 1 08


Octal subtraction1
Octal Subtraction

ex

3 5 3 68

- 2 4 5 78


Hexadecimal subtraction
Hexadecimal Subtraction

B 16

7 C 3 916

19

- 3 7 F 216

4 4 4 716


Hexadecimal subtraction1
Hexadecimal Subtraction

8 A D 416

- 5 D 616

16


Let s do some exercises

Let’s do some exercises!

Octal, Hexadecimal, Binary

Addition & Subtraction


ad