Skip to main content

PyTorch Code for Simple Neural Networks for MNIST Dataset

Radix Complement and Diminished Radix complement

Complements are used in digital computers for simplifying the subtraction and for logical manipulations. There are two types of complement

  • Radix complements ( r complement)
  • diminished radix complements (r-1 complement)

For base 2 or binary number system the r’s complement is 2’s complement and (r-1)’s complement is 1’s complement

For base 10 or decimal system the r’s complement is 10’s complement and (r-1)’s complement is 9’s complement.

10’s Complement

Let us assume the number 3567890, for finding the 10’s complement, there is a rule

3 5 6 7 8 9 0
Most significant Digit           Least Significant Digit

10’s complement can be obtained by

  • leaving all least significant 0’s unchanged
  • subtracting the first non zero least significant digit from 10
  • and subtracting all higher significant digits from 9

For the above example, The 10’s complement is

Given number 3 5 6 7 8 9 0
Process 9-3 9-5 9-6 9-7 9-8 10-9 unchanged
10’s Complement 6 4 3 2 1 1 0

so 10’s complement of 3567890 is 6432110

9’s Complement

9’s complement is a diminished radix complement and can be easily found out by subtracting all the given digits by 9.

For example, the 9’s complement of 3567890 is

9999999 – 3567890 = 6432109

given number 3 5 6 7 8 9 0
Process 9-3 9-5 9-6 9-7 9-8 9-9 9-0
9’s complement 6 4 3 2 1 0 9

In short,

10’s Complement = 9’s Complement + 1

2’s Complement

For binary numbers, there is 2’s complement and 1’s complement

2’s complement can be obtained by

  • leaving the least significant 0’s unchanged and the first 1 unchanged
  • replacing 1’s with 0’s and 0’s with 1’s in all other higher significant digits
given number 1 1 0 1 1 0 0
process 0 0 1 0 unchanged unchanged unchanged
2’s complement 0 0 1 0 1 0 0


2’s complement of 1101100 is 0010100

1’s complement

Finding 1’s complement is just to replace all 1’s by 0’s and all 0’s by 1’s

1’s complement of 1101100 is 0010011

in short

2’s complement = 1’s complement + 1


  1. very easy to understand and simlified form as well.

  2. Thank you so much! I really appreciate this because it helps me a lot to understand directly about the types of complement namely the radix and diminished radix complement.In fact, this is so resourceful.


Post a Comment

Popular posts from this blog

Installing ns3 in Ubuntu 22.04 | Complete Instructions

In this post, we are going to see how to install ns-3.36.1 in Ubuntu 22.04. You can follow the video for complete details Tools used in this simulation: NS3 version ns-3.36.1  OS Used: Ubuntu 22.04 LTS Installation of NS3 (ns-3.36.1) There are some changes in the ns3 installation procedure and the dependencies. So open a terminal and issue the following commands Step 1:  Prerequisites $ sudo apt update In the following packages, all the required dependencies are taken care and you can install all these packages for the complete use of ns3. $ sudo apt install g++ python3 python3-dev pkg-config sqlite3 cmake python3-setuptools git qtbase5-dev qtchooser qt5-qmake qtbase5-dev-tools gir1.2-goocanvas-2.0 python3-gi python3-gi-cairo python3-pygraphviz gir1.2-gtk-3.0 ipython3 openmpi-bin openmpi-common openmpi-doc libopenmpi-dev autoconf cvs bzr unrar gsl-bin libgsl-dev libgslcblas0 wireshark tcpdump sqlite sqlite3 libsqlite3-dev  libxml2 libxml2-dev libc6-dev libc6-dev-i386 libclang-dev llvm-

Installation of NS2 (ns-2.35) in Ubuntu 20.04

Installation of NS2 (ns-2.35) in Ubuntu 20.04 LTS Step 1: Install the basic libraries like      $] sudo apt install build-essential autoconf automake libxmu-dev Step 2: install gcc-4.8 and g++-4.8 open the file using sudo mode $] sudo nano /etc/apt/sources.list Include the following line deb bionic main universe $] sudo apt update $] sudo apt install gcc-4.8 g++-4.8 Step 3:  Unzip the ns2 packages to home folder $] tar zxvf ns-allinone-2.35.tar.gz $] cd ns-allinone-2.35/ns-2.35 Modify the following make files. ~ns-2.35/ Change @CC@ to gcc-4.8 change @CXX@ to g++-4.8 ~nam-1.15/ ~xgraph-12.2/ ~otcl-1.14/ Change in all places  @CC@ to gcc-4.8 @CPP@ or @CXX@ to g++-4.8 open the file: ~ns-2.35/linkstate/ls.h Change at the Line no 137  void eraseAll() { erase(baseMap::begin(), baseMap::end()); } to This void eraseAll() { this->erase(baseMap::begin(), baseMap::end()); } All changes made Step 4: Open a new termi

Installation of NS2 in Ubuntu 22.04 | NS2 Tutorial 2

NS-2.35 installation in Ubuntu 22.04 This post shows how to install ns-2.35 in Ubuntu 22.04 Operating System Since ns-2.35 is too old, it needs the following packages gcc-4.8 g++-4.8 gawk and some more libraries Follow the video for more instructions So, here are the steps to install this software: To download and extract the ns2 software Download the software from the following link Extract it to home folder and in my case its /home/pradeepkumar (I recommend to install it under your home folder) $ tar zxvf ns-allinone-2.35.tar.gz or Right click over the file and click extract here and select the home folder. $ sudo apt update $ sudo apt install build-essential autoconf automake libxmu-dev gawk To install gcc-4.8 and g++-4.8 $ sudo gedit /etc/apt/sources.list make an entry in the above file deb bionic main universe $ sudo apt update Since, it&#