NAND NAND realization is a concept under which we draw a logic circuit by using only NAND gates. The basic logic gates include – NAND gate, NOR gate, OR gate, XOR gate, AND gate and NOT gate. Among these NAND gate and NOR gate are universal gates, it means we can make an other logic gate using these two gates. In NAND NAND realization the input, output and the truth table of the logical expression remains same, just the circuit gets changed. The changed circuit contains only NAND gate.
In this article we are going to see how can we make or convert any given logical expression or circuit by using only NAND gate.
Before we start, let’s recap the working of basic logic gates with their truth table.
AND Gate
An AND gate multiplies the given input and show them in the output. It has multiple inputs and only one output.
Truth table for AND gate
| A | B | Y |
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Output ( Y ) = A.B
Here, A, B are inputs and Y is the output.
OR Gate
The OR gate adds the given input and shows them in the output. This gate also has multiple inputs and only one output.
Truth table for OR gate
| A | B | Y |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
Output ( Y ) = A + B
Here, A, B are inputs and Y is the output.
NOT Gate
A NOT gate inverts the input and show it in the output. It has only one input and only one output.
Truth table for NOT gate
| Input | Output |
| 1 | 0 |
| 0 | 1 |
NAND Gate
A NAND gate is a combination of AND gate + NOT gate. This gate also has many inputs and only one output.
Truth table for NAND gate
| A | B | Y |
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
Output ( Y ) = (AB)’
NOR Gate
A NOR gate is a combination of OR gate + NOT gate. NOR gate also has many inputs and only one output.
Truth Table
| A | B | Y |
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 0 |
Output ( Y ) = ( A + B )’
XOR Gate
A logic gate with many inputs and one output.
Truth Table
| A | B | Y |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
When both inputs are same, output is zero. And when any of two input is 1 then output is 1.
Output ( Y ) = ( A ⨁ B )
NAND NAND Realization
Now lets see how can we convert basic logic gates circuit to only NAND gate circuit.
NOT gate using NAND gate
The input terminals of NAND gate are shorted to make it OR gate. This circuit verifies the truth table of NOT gate.
AND gate using NAND gate
AND gate is obtained by using NAND gate and NOT gate ( made using NAND gate ) in series.
OR gate using NAND gate
OR gate is made as shown in the figure below.
The input A and B are inverted using NOT gate ( made using NAND gate ), then A’ B’ is applied as input in other NAND gate.
The circuit shown above generates the
output ( A’B’ )’
this can be written as –
A’’ + B’’ = A + B ( OR gate )
XOR gate using NAND gate
The circuit for XOR using NAND is –
The output obtained is [(A’B)’ (AB’)’]’
Y = [ (A’B) + (AB’) ]’’
Y = A’B + AB’ = ( A ⨁ B )
Procedure for NAND NAND Realization
1 : Simplify the given logical expression and then convert it in the SOP form.
2 : Draw the circuit for the expression using basic logic gates.
3 : Now replace every normal gates by the gates we made using only NAND gate.
4 : Draw the final circuit using only NAND gates.
Example
Q. Draw Y ( m ) = A’B’ + B’C
The given expression is already in SOP form and simplified. So first step is done.
Circuit using basic logic gates
Transformed circuit using only NAND gate
The output obtained is = [(A’B’)’ (B’C)’]’
= [ (A’B’) + (B’C) ]’’
= A’B’ + B’C
Author
Akash Sharma
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