Prove that the dual of the exclusive-OR gate is also itscomplement
1 answer:
Answer:
Explanation:
The dual of a function means replace AND with OR and replace OR with AND.
XOR gate of A , B is
So, Dual of A XOR B is ( replace AND with OR and OR with AND)
Complement of A XOR B is (In finding compliment AND becomes OR and OR becomes AND ).
By inter changing the above product of terms
Complement of
So, Dual of A XOR B = Complement of A XOR B.
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The question is not complete! Here is the complete question and its answer!
Create a lottery game application. Generate three random numbers (see Appendix D for help in doing so), each between 0 and 9. Allow the user to guess three numbers. Compare each of the user’s guesses to the three random numbers and display a message that includes the user’s guess, the randomly determined three-digit number, and the amount of money the user has won as follows:
no matches: 0
any one matching: 10$
two matching: 1000$
three matching: 100000$
Code with Explanation:
#include <iostream>
using namespace std;
int main()
{
int matches=0;
int guess_1, guess_2, guess_3;
int num_1, num_2, num_3;
// get 3 digits from the user
cout<<"Enter first guess digit 0 to 9"<<endl;
cin>>guess_1;
cout<<"Enter second guess digit 0 to 9"<<endl;
cin>>guess_2;
cout<<"Enter third guess digit 0 to 9"<<endl;
cin>>guess_3;
// every time program runs srand() generates new random numbers and rand()%10 makes sure that number is single digit 0 to 9
srand(time(NULL));
num_1=rand()%10;
cout<<"First lottery digit: "<<num_1<<endl;
num_2=rand()%10;
cout<<"Second lottery digit: "<<num_2<<endl;
num_3=rand()%10;
cout<<"Third lottery digit: "<<num_3<<endl;
// store random generated numbers and guess numbers in arrays to compare them
int num[3]= {num_1,num_2,num_3};
int guess[3]={guess_1,guess_2,guess_3};
// compare the arrays to find out how many are matching
for(int i=0; i<3; i++)
{
for(int j=0; j<3; j++)
{
if(num[i]==guess[j])
{
matches = matches + 1;
}
}
}
cout << "Total Matches are: " <<matches << endl;
// display reward according to the number of matches
if (matches==0)
cout<<"you won: $0"<<endl;
if (matches==1)
cout<<"you won: $10"<<endl;
if (matches==2)
cout<<"you won: $1000"<<endl;
if (matches==3)
cout<<"you won: $100000"<<endl;
return 0;
}
Output:
Enter first guess digit 0 to 9
7
Enter second guess digit 0 to 9
1
Enter third guess digit 0 to 9
5
First lottery digit: 3
Second lottery digit: 7
Third lottery digit: 2
Total Matches are: 1
You won: $10
Enter first guess digit 0 to 9
7
Enter second guess digit 0 to 9
3
Enter third guess digit 0 to 9
4
First lottery digit: 5
Second lottery digit: 4
Third lottery digit: 7
Total Matches are: 2
You won: $1000
