Skip to main content

Canonical Forms and Standard Forms

Standard Forms

  • each term in the function can have any number of literals.

Example, F1 = a +b’c + cde

  • There are 5 variables in F1 (a,b,c,d,e)
  • Canonical form terms should be written as m0, m1… (sum of Products) or M0, M1, M2… (Product of sums).
  • Each term in the canonical form should have all the literals.

Example: F1 = ab’c’d’e’ + abcd’e’ + abcde

More about Canonical Forms

Minterms

  • It is Sum of Products
  • Canonical form is Sum of Minterms
  • three variable minterms are shown below
x a b c minterms
0 0 0 0 m0=a’.b’.c’
1 0 0 1 m1=a’.b’.c
2 0 1 0 m2=a’.b.c’
3 0 1 1 m3=a’.b.c
4 1 0 0 m4=a.b’.c’
5 1 0 1 m5=a.b’.c
6 1 1 0 m6=a.b.c’
7 1 1 1 m7=a.b.c

Maxterms

  • Product of Sum (PoS)
  • Canonical form is Product of MaxTerms
  • three variable maxterms are shown below
x a b c minterms
0 0 0 0 M0=(a+b+c)
1 0 0 1 M1=(a+b+c’)
2 0 1 0 M2=(a+b’+c)
3 0 1 1 M3=(a+b’+c’)
4 1 0 0 M4=(a’+b+c)
5 1 0 1 M5=(a’+b+c’)
6 1 1 0 M6=(a’+b’+c)
7 1 1 1 M7=(a’+b’+c’)

usually

Mi = (mj)’

Express the boolean function F = A + BC in a sum of minterms.

The function has three variables,

so F = A + BC will be

F = A(B + B’) + (A +A’) BC  [since, x + x’ =1]

F = AB + AB’ + ABC + A’BC

F = AB(C+C’) + AB’(C+C’) + ABC + A’BC

F = ABC + ABC’ + AB’C + AB’C’ + ABC + A’BC

F = ABC + ABC’ + AB’C + AB’C’ + A’BC [since x + x = x]

F= m0 + m6 + m5 + m4 + m3

Comments

  1. wonderful explanation. plz do visit this page once. its really helpful.

    ReplyDelete

Post a Comment

Popular posts from this blog

Ant Colony algorithm using NS2

Ant Colony Algorithm in NS2 for Wired Networks. Please follow the video for full instructions  I am running in Ubuntu 20.04 There are multiple files in Ant Colony (we use a protocol called Antnet) which i have already included in my blog called https://www.nsnam.com  Lets go to my Blog. And Search for Ant Colony and Download the complete folder AntNet as shown in the video. Now Copy paste the files in their corresponding location: My Location if ns2 is  /home/pradeepkumar/ns-allinone-2.35/ns-2.35/ Inside this folder, the files have to be pasted in differnet sub folders...  Let me show you one by one... cmu-trace.cc and cmu-trace.h have to be pasted to ~trace/ drop-tail.cc and drop-tail.h ---- ~queue/ Makefile.in to be replaced in the ns-2.35/ folder. ns-default.tcl, ns-lib.tcl and ns-packet.tcl to be pasted at  ~tcl/lib packet.h to be replaced at common/ folder. priqueue.cc and priqueue.h to be pasted at queue/ antnet / folder have to be copied to ns-2.35/ folder (this is very imp

Installing NS-3.32 in Ubuntu 20.04

This is about installing ns version 3.32 in Ubuntu 20.04 LTS. #ns3 #ns3 .32 #networksimulation The commands used in the video are given here. $] sudo apt update $] sudo apt install build-essential autoconf automake libxmu-dev python3-pygraphviz cvs mercurial bzr git cmake p7zip-full python3-matplotlib python-tk python3-dev qt5-qmake qt5-default gnuplot-x11 wireshark Download the ns-allinone-3.32.tar.bz2 package from nsnam.org and copy it to /home/ folder See the full video for detailed instructions Extract it either in GUI or using command $] tar jxvf ns-allinone-3.32.tar.bz2 $] cd ns-allinone-3.32/ $] ./build.py --enable-examples --enable-tests The above command will take some time to install all the packages  You can see the output as shown below ns3 To check whether ns3 installed successfully, use the following commands. $] cd ns-3.32/ $] ./waf --run hello-simulator You should get the output as Hello Simulator $] ./waf --run first This is the example from the ns-3.32/exa

ns3 installation in Ubuntu 16.04

This post serves the installation instructions of ns3 in ubuntu 16.04 version. Some of my students are working in ns3, this post will benefit them in installing ns3. OS Used: Ubuntu 16.04.4 ns3 version: ns3 version 3.27 The same procedure will be applied for OS like Debian, Linux Mint. Fresh installation of Ubuntu 16.04 Let you try the fresh installation of ubuntu in your hard disk along with windows. Installation of ns3 dependencies ns3 needs so many dependencies, developmental libraries, drivers, etc. so install all those $] sudo apt update  $] sudo apt upgrade $] sudo apt-get install build-essential autoconf automake libxmu-dev python-pygoocanvas python-pygraphviz cvs mercurial bzr git cmake p7zip-full python-matplotlib python-tk python-dev python-kiwi python-gnome2 python-gnome2-desktop-dev python-rsvg qt4-dev-tools qt4-qmake qt4-qmake qt4-default gnuplot-x11 wireshark The above command make take some time to download, compile and install it, Be Patie