Question

How will you obtain OR, AND gates from the NAND and NOR gates? Write symbol, Boolean formula and truth table.

Answer 1

(i) To obtain AND gates from NAND gates:

For obtaining AND gate from NAND gate the output of NAND gate is connected to the input (obtained from NAND gate by joining the two inputs).
For obtaining OR gate from NAND gate the inputs $A$ and $B$ are connected to the two NOT gates obtained from NAND gates. The input get inverted as $\overline{A}$ and $\overline{B}$. These inputs are then fed to the NAND gate as shown in fig. drawn below.
Boolean formual: $y=\overline{y}=\overline{\overline{A\cdot B}}=A\cdot B$

Input

Output

A	B	y	y
0 1 0 1	0 0 1 1	1 1 1 0	0 0 0 1

(ii) To obtain OR gate from NAND gate:

For obtaining OR gate from NAND gate the input $A$ and $B$ are connected to the two NOT gates obtained from NAND gates. The input gate inverted as $\overline{A}$ and $\overline{B}$. These inputs are then fed to the NAND gate as shown in fig, drawn belows.
Boolean formula: $y=\overline{\overline{A}}\overline{\overline{B}}=\overline{\overline{A}}+\overline{\overline{B}}=A+B$

Input

Output

A 0 1 0 1

B 0 0 1 1

$\overline{A}$ 1 0 1 0

$\overline{B}$ 1 1 0 0

y 0 1 1 1

(iii) To obtain OR gate from NOR gate:

To obtain OR gate from NOR gate the inputs are connected to NOR gate which in turn is again connected to NOR gate.

Input	Output
A	$\overline{A}$
0 1	1 0

(iv) To obtain AND gate from NOR gate:

To obtain AND gate from NOR gate the inputs are connected to NOT gate obtained from NOR gate giving inverted $A\left(\overline{A}\right)$ and inverted $B\left(\overline{B}\right)$.
Which is inturn are again connected is NOR gate.
Boolean formula: $\overline{y}=\overline{A}+\overline{B}=\overline{\overline{A}+\overline{B}}=A\cdot B$