How do you make an NOT Gate from a NAND Gate A NOR Gate from

How do you make an NOT Gate from a NAND Gate? A NOR Gate from a NAND Gate? An XOR Gate from a NAND Gate? For the comparison of two four bit numbers that differ in the MSB (Most Significant Bit), is it necessary to compare the remaining 3 bits to obtain the comparison result (given the result of the MSB comparison)?

Solution

Ans)

2) What NOT gate does input A output A\'

let\'s take 2 input NAND gate input A B output (AB)\',if we made A=B we will get A\',that makes a NOT gate from NAND gate

So short the both inputs of NAND gate and give input A to it ,it works as NOT gate

----------

Using Demorgan\'s thoerem (A+B)\'=(A\'B\')\'

So NOR gate output is (A+B)\' =(A\'B\')\',we need A\' and B\' we can get them by using NOT gate made using NAND gate from above explanation then give the A\' and B\' to NAND gate to get (A\'B\')\'=NOR Gate

--------------------------

XOR output =A\'B+AB\'=((A\'B+AB\')\')\' using identity (A\')\'=A

=((A\'B)\'(AB\')\')\' using Demorgan laws

We get A\' by using NOT gate made by NAND gate

Similarly B\' is obtained

NOW give A\' and B to 1 NAND Gate and A and B\' to another NAND gate ,output of each of then to another NAND gate ,so total 5 NAND gates are required to get XOR with NAND gate here

---------------------------

Only 1 question per post will be answered please ,but I giving brief answer to 3 here

3)Yes we don\'t need other bit\'s to compare when MSB of each number differs ,because MSB holds the Max value ,we can say from that whether which number big or small