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C++ program to implement Booth's multiplier

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  1  #include <iostream>
  2  #include <windows.h>
  3  #include <fstream>
  4  #include <math.h>
  5  #define pause system("pause");
  6  using namespace std;
  7  const int no_of_bits = 32;
  8  /* this Program uses Following notations.... first bit for signed and then it goes like this 1 2 4 8 16 32 64......
  9  /* ----------------------------------------global variables ----------------------------------
 10  */
 11  int Q1=0; /// extra bit holder
 12  int A[no_of_bits]; /// Accumulator storing array
 13  int Q[no_of_bits];/// Multiplier storing Array.
 14  int N,Qsize;/// no of bits in multiplier
 15  int X; /// no of bits in multiplicand.
 16  int M[no_of_bits]; /// M value
 17  int M2Complement[no_of_bits];/// -M
 18  int temp[no_of_bits]; /// for temporary use
 19  ofstream out;
 20 
 21  /*
 22  ...............................................now function ....................................
 23 
 24  */
 25  int binary_convert(int,int m[]);
 26  void ARS(); /// arithmetic Right Shift ...
 27 
 28  void Add(int[],int []); /// used for Function two's complement... and adding of two array
 29  void intialiser(int ,int ); /// used to initialize A Q N and all
 30  a
 31 
 32  /*
 33 
 34 
 35  Main Function Starts
 36 
 37 
 38  */
 39  int main ()
 40  {int multiplicand,multiplier,result=0;
 41  out.open("Booth's Multiplier.txt",ios::out);
 42  out<<"++++++++++++++++++++++++++++++++++++++++Welcome To booth's Multiplier++++++++++++++++++++++++++++\n";
 43  cout<<endl;
 44  /// m is the multiplicand
 45  /// is multiplier....
 46  cout<<"                          Booth's multiplier                                 \n\n\n\a\n";
 47  cout<<"============================================================================\n";
 48  cout<<"Enter the Multiplicand ---> ";
 49  out<<"\n\n\n\n============================================================================\n";
 50  out<<"Enter the Multiplicand ---> ";
 51 
 52  cin>>multiplicand;
 53  out<<multiplicand;
 54  cout<<"Enter the Multiplier ---> ";
 55  cin>>multiplier;
 56  cout<<"Displaying Result of "<<multiplicand<<"X"<<multiplier<<endl;
 57  out<<"\nEnter the Multiplier ---> "<<multiplier<<endl;;
 58  out<<"Displaying Result of "<<multiplicand<<"X"<<multiplier<<endl;
 59 
 60  out<<"============================================================================\n";
 61 
 62  cout<<"============================================================================\n";
 63 
 64  int opr=0;
 65  /*
 66  opr code ...
 67  opr code =1 shifting
 68  opr =2 Subs
 69  opr=3 Add...
 70  */
 71  int counter=0;
 72  intialiser(multiplicand,multiplier);
 73 
 74 
 75 
 76  cout<<"============================================================================\n\n                ::StepS::\n\n";
 77  cout<<"============================================================================\n";
 78 
 79  out<<"============================================================================\n\n                ::StepS::\n\n";
 80  out<<"============================================================================\n";
 81 
 82 
 83 
 84  cout<<"Index\t A\t\tQ\t\tQ1\tN\t operation\n\n";
 85  cout<<"0\t";
 86  out<<"Index\t A\t\tQ\t\tQ1\tN\t operation\n\n";
 87  out<<"0\t";
 88  for(int i=no_of_bits-X;i<no_of_bits;i++){
 89  cout<<A[i];out<<A[i];}cout<<"\t\t"; out<<"\t\t";
 90  for(int i=no_of_bits-N;i<no_of_bits;i++){
 91  cout<<Q[i];out<<Q[i];}
 92  cout<<"\t\t"<<Q1<<"\t"<<N<<"\t ------------";; out<<"\t"<<Q1<<"\t"<<N<<"\t -------------";
 93 
 94 
 95 
 96 
 97 
 98  while(N>0){
 99 
100 
101 
102 
103  if(Q[no_of_bits-1]==1&&Q1==0) /// it is of form 10
104  {Add(A,M2Complement);opr=2;
105 
106  }
107  else if (Q[no_of_bits-1]==0&&Q1==1) /// it is of form 01
108  {
109      Add(A,M);opr=3;
110  }
111  ARS(); /// shifting at last..
112   cout<<"\n\a____________________________________________________________________________________________________________________\n";
113  cout<<++counter<<"\t";
114  out<<"\n\a____________________________________________________________________________________________________________________\n";
115  out<<++counter<<"\t";
116 
117 
118  for(int i=no_of_bits-X;i<no_of_bits;i++){out<<A[i];
119  cout<<A[i];} cout<<"\t\t";out<<"\t\t";
120  for(int k=(no_of_bits-Qsize);k<no_of_bits;k++) {cout<<Q[k];out<<Q[k];}
121  cout<<"\t\t"<<Q1<<"\t"<<N<<"\t";out<<"\t\t"<<Q1<<"\t"<<N<<"\t";
122  if(opr==1){cout<<"\tShifting"<<endl;out<<"\tShifting"<<endl;}
123  else if(opr==2){ cout<<"\tSubtracting and Arithmetic Shifting....\n";out<<"\tSubtracting and Arithmetic Shifting....\n";}
124  else {cout<<"\tAdding and Shifting....\n";out<<"\tAdding and Shifting....\n";}
125  out<<"\n\a____________________________________________________________________________________________________________________\n";
126  cout<<"\n\a____________________________________________________________________________________________________________________\n";
127 
128  }
129  int power=0;
130  if(A[0]==0) /// it is a +ve result
131  {
132 
133      for(int k=no_of_bits-1; k>=(no_of_bits-Qsize);k--)
134 
135  {result=result+(pow(2,power++)*Q[k]);
136 
137  }
138   for(int k=no_of_bits-1; k>=(no_of_bits-X);k--)
139  {
140      result=result+(pow(2,power++)*A[k]);
141 
142  }
143 
144 
145 
146  }
147  else  /// if number is negative
148  {int product[X+Qsize],tempproduct[X+Qsize];
149  int prosize=X+Qsize,sum=0,carry=0;
150  cout<<" Answer is negative so Taking its Two's Complement..\n";
151 
152  for(int i=0;i<X+Qsize;i++) tempproduct[i]=0; temp[(X+Qsize)-1]=1;
153 
154  for(int k=0;k<Qsize;k++) product[--prosize]=Q[(no_of_bits-1)-k];
155  for(int k=0;k<X;k++) product[--prosize]=A[(no_of_bits-1)-k];
156 
157 
158  for(int i=(Qsize+X-1);i>=0;i--)
159      if(product[i]==0)product[i]=1;
160  else product[i]=0;
161  for(int i=(X+Qsize-1);i>=0;i--)
162      {sum=0;
163      sum=carry+product[i]+tempproduct[i];
164      if(sum==3)
165          {
166              sum=1;carry=1;
167          }else if(sum==2)
168          {
169              sum=0;carry=1;
170          }
171          else{
172              carry=0;
173          }
174          product[i]=sum;
175 
176      }
177  int power=0;
178  for(int i=(Qsize+X)-1;i>=0;i--)
179  {
180      result=result+(product[i]*pow(2,power++));
181  }
182 
183 
184  result=(result*-1)-1;
185  }
186 
187  cout<<"Result=="<<result<<endl;
188  out<<"Result=="<<result<<endl;
189 
190  out.close();
191  cout<<"\n";
192  pause;
193 
194 
195  }
196  void intialiser(int m ,int q)
197  {
198 
199  for(int i=0;i<no_of_bits;i++)
200  {
201      Q[i]=0;
202      A[i]=0;
203      temp[i]=0;
204      M[i]=0;
205      M2Complement[i]=0;
206 
207  }
208 
209 
210 
211  X=binary_convert(m,M);
212 
213  N=binary_convert(q,Q);
214  Qsize=N;
215  m=m*(-1);
216  X=binary_convert(m,M2Complement);
217 
218  out<<"\n==========================================================================\n";
219  out<<"\n M =\t";
220 
221  cout<<"\n==========================================================================\n";
222  cout<<"\n M =\t";
223  for(int i=no_of_bits-X;i<no_of_bits;i++){
224  cout<<M[i];out<<M[i];}
225  cout<<"\n Q =\t";
226  out<<"\n Q =\t";
227 
228  for(int i=no_of_bits-N;i<no_of_bits;i++){
229  cout<<Q[i];out<<Q[i];}
230  cout<<"\n A =\t";
231  out<<"\n A =\t";
232 
233  for(int i=no_of_bits-X;i<no_of_bits;i++){
234  cout<<A[i];out<<A[i];}
235  cout<<"\n-M =\t";
236  out<<"\n-M =\t";
237 
238  for(int i=no_of_bits-X;i<no_of_bits;i++)
239  {
240  cout<<M2Complement[i];out<<M2Complement[i];}cout<<"\n==========================================================================\n";
241 
242  out<<"\n==========================================================================\n";
243 
244  }
245 
246 
247 
248 
249 
250 
251 
252  void ARS()
253  {
254 
255  Q1=Q[no_of_bits-1];
256  for(int i=no_of_bits-1;i>0;i--)
257  {
258      Q[i]=Q[i-1];
259  }
260  for(int i=0;i<=(no_of_bits-Qsize);i++)
261  Q[i]=A[no_of_bits-1];
262  for(int i=no_of_bits-1;i>0;i--)
263  {
264      A[i]=A[i-1];
265  }
266 
267 
268 
269  N--; /// decreasing N value.
270  }
271 
272  int binary_convert(int num,int m[])
273  {bool ispositive=false;int counter=(no_of_bits-1),bitsize=0; /// counter will be used to set current bit value..
274 
275      if(num>0)
276      {
277          ispositive=true;
278      }
279 
280      if(ispositive==true) m[0]=0; /// setting signed bit ;;
281      else
282 
283      {
284          m[0]=1;
285      num=num*(-1);
286      }
287      while(num>0)
288      {bitsize++;
289          if(num%2==0) m[counter]=0;
290          else m[counter]=1; /// reminder ones....
291 
292  num=num/2;
293 
294  counter--;
295 
296      }
297      if(ispositive==false) /// i.e number is negative
298 
299  {
300          for(int counter=1;counter<no_of_bits;counter++)
301 
302          {
303              if(m[counter]==0) m[counter]=1;
304              else m[counter]=0;
305 
306          } /// taking One's Complement...
307 
308          for(int i=0;i<no_of_bits;i++)
309 
310          {if(i==(no_of_bits-1)) temp[i]=1;
311          else temp[i]=0;
312 
313 
314          } /// adding one...
315          Add(m,temp);
316 
317      }
318 
319  return (bitsize+1);
320  }
321  void Add(int FirstNumber[],int SecondNumber[] )
322  {int carry=0,sum=0;
323 
324  for(int i=(no_of_bits-1);i>=0;i--)
325  {sum=0;
326  sum=FirstNumber[i]+SecondNumber[i]+carry;
327 
328  if(sum==3)
329  {
330      sum=1;carry=1;
331  }else if(sum==2)
332  {
333 
334      sum=0; carry=1;
335  }
336  else
337  {
338      carry=0;
339  }
340 
341      FirstNumber[i]=sum;
342  }
343  }
get the source code

https://drive.google.com/file/d/0BwyIMs3NcEzYdE9QRThUTjh4WjQ/view?usp=sharing

get the executable.
.EXE


https://drive.google.com/file/d/0BwyIMs3NcEzYSTk1Y3lGOXM0LU0/view?usp=sharing



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