SIMPLEST Way to Realize Different Logic Gates Using NAND/NOR

 

SIMPLEST Way to Realize Different Logic Gates Using NAND/NOR  Logic Gates

Hello this is Jay and welcome to Engineers’ Burger once again. On the road of pursing the engineering stream we simplify problems and deliver the best solutions. In this post you will learn how to realize any of the 7 basic logic gates using the universal logic gates NAND and NOR gates in the simplest way possible. Before we proceed any further following are some things you need to understand first or know them thoroughly in order to completely understand what is happening. 

BASIC CONCEPTS OF LOGIC GATES YOU MUST KNOW: 

They may sound trivial and you may feel you already know them, but we often forget that these rules have a great depth in their meanings so do skim through them at least once!

1. A logic gate has ATLEAST 2 inputs except NOT Gate which has only 1 input.

2. A logic gate has only and only one single output.

3. NOT gate acts like INVERTER. It gives output 0 for input 1 and vice versa. So basically,
When you attach a NOT gate to AND gate we get NAND gate.
When you attach a NOT gate to NAND gate we get back AND gate.
This applies for all the gates,
 i.e OR+NOT=NOR,
 NOR+NOT=OR,
 XOR+NOT=XNOR
…and so on.

4. You must know that
NAND is the inverted gate of AND.
NOR is the inverted gate of OR
XNOR is the inverted gate of XOR.
“Inverted gate” means output of NAND and AND gates are exactly opposite. For some input, o/p of AND is 1 then for same input, o/p of NAND is 0.

5. I assume you already know what are AND, OR, NOT, NOR, NAND, XOR, XNOR logic gates.

Now having understood the above things thoroughly, you must easily understand what is being done below.

1. Realize NOT gate - using NAND / NOR

 Formation we use is,

 

• Use NAND gate or NOR gate in place of the above black box and you will form a NOT gate.
•  Inputs A and B are shorted.

2. Realize AND gate - using NAND
Realize OR gate - using NOR

Formation we use is,

 

•  Use NAND gates in place of the above black boxes and you will form a AND gate.
• Use NOR gates in place of the above black boxes and you will form a OR gate.
• Explanation: What we have done is we have attached a NOT gate (made from NAND/NOR) to NAND gate to get AND gate. (The inverting effect as explained in point 3 above in BASIC CONCEPTS OF LOGIC GATES YOU MUST KNOW), i.e
  NAND+NOT=AND
  NOR+NOT=OR

3. Realize AND gate – using NOR
Realize OR gate – using NAND

We use ROCKET formation (I named it!),

 

•  Use NAND gates in place of the above black boxes and you will form a OR gate.
• Use NOR gates in place of the above black boxes and you will form a AND gate.
• Explanation: We have fed the inputs A and B into NOT gates (made from universal gates) whose outputs are fed to another universal gate.
•  For quick calculations, remember the above formation of gates as a ROCKET formation (coz, the above block diagram looks like a laid rocket!)

4. Realize NAND using NOR
Realize NOR using NAND

•  Use NAND gates in place of the above black boxes and you will form a NOR gate.
•  Use NOR gates in place of the above black box and you will form a NAND gate.
•  Explanation: We have just attached a NOT gate in rocket formation shown in point 3 above to invert AND to NAND and OR to NOR. ( Remember, AND+NOT=NAND…)

5. Realize XOR -  using NAND
Realize XNOR - using NOR

We use Kajukatri formation (The block diagram of gates given below looks like ‘Kajukatri’-Indian sweet having a shape of a diamond. The black boxes form the corners of a diamond, hence Kajukatri)

 

•  Use NAND gates in place of the above black boxes and you will form a XOR gate.
•  Use NOR gates in place of the above black box and you will form a XNOR gate.

6. Realize XNOR – using NAND
Realize XOR – using NOR

•  Well I am not drawing the block diagram for this one! (Tiresome!) But it’s simple, just add a NOT gate (made from respective NAND/NOR gate) to o/p of the above KAJUKATRI formation, and you will get respective inverted gates.
  i.e XOR + NOT = XNOR and XNOR + NOT = XOR (The inverting effect as explained in point 3 above in BASIC CONCEPTS OF LOGIC GATES YOU MUST KNOW.)

ALL the GATES are realized using each of the NAND and NOR universal gates!  For quick calculations and realizations, just remember the ROCKET formation (for NOR to AND and NAND to OR) and KAJUKATRI formation (for NAND to XOR and NOR to XNOR) and rest gates can be realized by just inserting a NOT gate (made from respective NOR or NAND gate) .

Shoot your doubts and suggestions in comment below. I will be happy to answer them all!