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What is a Universal Gate and Why NAND is called a Universal gate?

A Logic Gate which can infer any of the gate among Logic Gates. OR a gate which can be use to create any Logic gate is called Universal Gate
We have following Logic Gates
NOT
AND
OR
NAND
NOR
XOR
XNOR
NAND and NOR Gates are called Universal Gates because all the other gates can be created by using these gates
In this post, we will see to how to make all other logic gates by using the NAND Gate
1. NAND gate to NOT Gate conversion
Refer the following diagram –
Digital : Image – NAND to NOT

Nand to Not conversion

Here the same input is applied to the both inputs of a NAND Gate
According to NAND Gate – If A and B are two inputs than output equation will be (A.B)’
For this case :
= (X.X)’
= X’
2. NAND Gate to AND Gate Convertion
Refer following diagram for NAND to and Gate conversion -
Digital : Image – NAND to AND

NAND to AND conversion

For this case – x and y are the two inputs to a NAND gate and the output of the First NAND gate goes again to an another NAND gate’s inputs.
=> s1 = (X.Y)’
=> s2 = (s1.s1)’ = s1’
=> s2 = ((X.Y)’)’
=> X.Y
3. NAND Gate to OR Gate Conversion
Refer the following Diagram
Digital : Image – NAND to OR

NAND to OR Conversion

According to diagram –
s1 = (X.X)’ = X’
s2 = (Y.Y)’ = Y’
s3= (s1.s2)’ = (X’.Y’)’
=> (X’)’ + (Y’)’
=> X+Y
4. NAND Gate to NOR Gate Convertion
Refer the following Diagram
Digital : Image – NAND to NOR

NAND to NOR conversion

According to diagram –
s1 = (X.X)’ = X’
s2 = (Y.Y)’ = Y’
s3= (s1.s2)’ = (X’.Y’)’
=> (X’)’ + (Y’)’
=> X+Y
s4 = (s3.s3)’ = s3’
=> (X + Y)’

What is a Universal Gate and Why NOR is called a Universal gate?

This is a continuation of previous post, in this post, we will see the NOR gate as a univarsal gate and create different gates using NOR gate.
As we know that NAND and NOR Gates are called Universal Gates since they can cerate any of the Logic Gate
Lets see to how to make all other logic gates by using the NOR Gate
1. NOR gate to NOT Gate conversion
Refer the following diagram –
Digital : Image – NOR to NOT

NOR to NOT Conversion

Here the same input is applied to the both inputs of a NOR Gate
According to NOR Gate – If A and B are two inputs than output equation will be (A+B)’
For this case :
= (X+X)’
= X’
= Inverted Input
2. NOR Gate to AND Gate Convertion
Refer following diagram for NOR to AND Gate conversion -
Digital : Image – NOR to AND Conversion

NOR to AND Conversion

According to diagram –
s1 = (X+X)’ = X’
s2 = (Y+Y)’ = Y’
s3= (s1+s2)’ = (X’+Y’)’
=> (X’)’ .(Y’)’
=> X.Y
=> AND Gate
3. NOR Gate to OR Gate Convertion
Refer the following Diagram
Digital : Image – NOR to OR Convertion

NOR to OR

For this case – X and Y are the two inputs to a NOR gate and the output of the First NOR gate goes again to an another NOR gate’s inputs.
=> s1 = (X+Y)’
=> s2 = (s1+s1)’ = s1’
=> s2 = ((X+Y)’)’
=> X+Y
=> OR Gate
4. NOR Gate to NAND Gate Convertion
Refer the following Diagram
Digital : Image – NOR to NAND

NOR to NAND Conversion

According to diagram –
s1 = (X+X)’ = X’
s2 = (Y+Y)’ = Y’
s3 = (s1+s2)’ = (X’+Y’)’
=> (X’)’ .(Y’)’
=> X.Y
s4 = (s3 + s3)’
=> s3′
=> (X.Y)’
=> NAND Gate
5. NOR to XOR Gate
Digital : Image – NOR to XOR Gate Convertion
6. NOR to XNOR Gate
Digital : Image – NOR to XNOR Gate Convertion

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Program to print factorial upto 'n' number of terms where n is accepted by use(using function)

#include
#include
void fibo(int n);
void main()
{
 int n;
 clrscr();
 printf("\Enter Limit : \n ");
 scanf("%d", &n);
 fibo(n);
 getch();
}
void fibo(int n)
{
 int i ,a=0, b=1 , fib=0;
 for(i=0; i  {
  printf(" %d ", fib);
  fib = a+b ;
  a=b;
  b=fib;
 }
}

Write a program to find out pythagorean triplets in raange of 1 to 100

#include
#include
#include
void main()
{
 int s1,s2,hyp,ptriple=0;
 clrscr();
 printf(" Side1 ---- side2 ---- hypotenus\n");
 for(s1=0;s1<=100;s1++)
 {
  for(s2=0;s2<=100;s2++)
  {
   for(hyp=1;hyp<=100;hyp++)
   {
   ptriple=(s1*s1)+(s2*s2);
   hyp=hyp*hyp;
   if(hyp==ptriple)
   {
   hyp=sqrt(hyp);
   printf("\n%d ---- %d ---- %d ",s1,s2,hyp);
   }
   }
  }
 }
 getch();
}