To understand the conversion we have to first understand the working of individual gate-
1.NOT Gate- This is the simplest form of a digital logic circuit . It is also called as inverter. It consist of only one input and one output and input can only be binary number it may be one or zero. NOT gate is a logic element whose output stage is always the complement of the input stage means when you supply logic 1 we will logic 0 and vice versa. Now how many stage are possible is calculated by 2^{n} (where n is the number of input) means hear we have input equal to 1 so number of stage possible is 0 and 1 (2^{1}). Truth table of NOT gate is as follows-
Input(2^{1}) | Output |
A | NOT A |
0 | 1 |
1 | 0 |
2.AND Gate- It is logic circuit has two input and one output. The operation of gate is such that output of gate is binary 1 if and only if all input are binary 1. If any of the input is binary 0 we will receive output as binary 0. Truth table of AND gate are as follows-
Number of stage possible = 2^{n}
=2^{2} = 4
Input | Output |
A | B | A.B |
0 | 0 | 0 |
0 | 1 | 0 |
1 | 0 | 0 |
1 | 1 | 1 |
3.OR Gate- Or gate is another basic logic gate like AND gate it as two input and one output. The operation of gate is such that output of gate is binary 1 if any of the input is binary low and we will receive logic zero only when both the inputs are low. Truth table of OR gate are as follows-
Number of stage possible = 2^{n}
=2^{2} = 4
Input | Output |
A | B | A+B |
0 | 0 | 0 |
0 | 1 | 1 |
1 | 0 | 1 |
1 | 1 | 1 |
4.NOR Gate- The term NOR is a contraction of the expression NOT and OR gate. Therefore a NOR gate is an OR gate followed by the inverter. The operation of gate is such that output of gate is binary 1 if both the input is binary low and we will receive logic zero only when any of the inputs are high. Truth table and expression of NAND gate are as follows-
Input | Output |
A | B | NOT (A OR B) |
0 | 0 | 1 |
0 | 1 | 0 |
1 | 0 | 0 |
1 | 1 | 0 |
For understanding the conversion, one should know about De Morgan’s theorem- It states that complement of sum is equal to the product of the complements.
NOT (A OR B)= NOT (A) AND NOT (B) ---- EQ 1
In the circuits,
We have used two NOR gate and short the input of each gate so we will get output as
= NOT (A) OR NOT(B)
Now it is again supplied to another NOR gate and we will get output as-
= NOT[(NOT) (A)] OR [(NOT) (B)]
= [NOT(NOT)(A)] AND[ NOT(NOT)(B)] (From EQ 1)
= A.B