Question

Write down truth table and Boolean expression for NOR and NAND gates.

Hint:

To quickly remember the truth tables: - For \textbf{NOR}, the output is 1 only when \textbf{all inputs are 0}. - For \textbf{NAND}, the output is 0 only when \textbf{all inputs are 1}. They are the exact opposites of the OR and AND gates.

Answer 1

Step 1: Understanding the Concept:
NOR and NAND gates are known as universal logic gates. They are combinations of basic gates (OR, AND) with a NOT gate. 
- NOR = NOT + OR. It gives a high output (1) only when all its inputs are low (0). 
- NAND = NOT + AND. It gives a low output (0) only when all its inputs are high (1).

Step 2: NOR Gate Details:  
The NOR gate is an OR gate followed by a NOT gate. 
Boolean Expression: 
The expression for an OR gate with inputs A and B is \(A+B\). The NOR gate inverts this output. Therefore, the Boolean expression is:

\[ Y = \overline{A+B} \]

 

This is read as "Y equals NOT (A OR B)".

Truth Table:

Inputs		OR Output	NOR Output
A	B	A + B	Y = \(\overline{A + B}\)
0	0	0	1
0	1	1	0
1	0	1	0
1	1	1	0

Step 3: NAND Gate Details: 
The NAND gate is an AND gate followed by a NOT gate. 
Boolean Expression: 
The expression for an AND gate with inputs A and B is \(A \cdot B\). The NAND gate inverts this output. Therefore, the Boolean expression is:

\[ Y = \overline{A \cdot B} \]

 

This is read as "Y equals NOT (A AND B)".

Truth Table:

Inputs		AND Output	NAND Output
A	B	A \(\cdot\) B	Y = \(\overline{A \cdot B}\)
0	0	0	1
0	1	0	1
1	0	0	1
1	1	1	0

Step 4: Final Answer: 
The Boolean expressions and truth tables for NOR and NAND gates are provided as detailed above.