5.2 Numbering systems
Upcoming SlideShare
Loading in...5
×
 

5.2 Numbering systems

on

  • 1,719 views

 

Statistics

Views

Total Views
1,719
Views on SlideShare
1,710
Embed Views
9

Actions

Likes
0
Downloads
7
Comments
0

1 Embed 9

http://olympicairtraining.talentlms.com 9

Accessibility

Categories

Upload Details

Uploaded via as Microsoft PowerPoint

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment

5.2 Numbering systems 5.2 Numbering systems Presentation Transcript

  • Module 5: Digital Techniques and Electronic Instrument Systems 5.2 Numbering Systems
  • Number and Base  Base: How many symbols (digits) are used in the current numbering system?  e.g. if the base of a number is 10, we use (maximum) 10 symbols to display this number.  if the base of a number is 8, we use 8 symbols to display this number. (0, 1, 2, 3, 4, 5, 6, 7).  Examples: 1578, 1808210, 1001012.
  • MSD and LSD  In every numbering system, the value of a digit is determined not only by its symbol, but also by its position.  The first digit of a number is called Most Significant digit (MSD).  The last digit of a number is called Less Significant digit (LSD).  Example: 184470287 MSD LSD
  • Binary System Rules  0 + 0 = 0  1 + 0 = 1  0 + 1 = 1  1 + 1 = 0 and 1 carry.  0 – 0 = 0  1 – 0 = 1  0 – 1 = 1 with 1 carry  1 – 1 = 0  Complementary subtraction:  Get the complementary of the subtrahend.  Add 1  Make addition  Discard any carries that exceed the size of the minuend.
  • Numbering System Conversions  Decimal to digital:  I divide the decimal number by 2  I repeatedly divide the result by 2, until the dividend becomes zero.  The residue of each division in reverse order is the binary number.  Digital to decimal:  In the first digit d0 of the binary number I assign d0 *20.  In the nth digit of the binary number I assign dn *2n.  The sum: d0*20+ d1*21 + … + dn*2n is the decimal number.  Octal, Hex number conversion:  The same methodology, but “2” is replaced with “8” and “16” respectively.