The NAND gate output will be low if the two inputs are-
1, 1
Understanding NAND Gate Output Logic
A NAND gate is a fundamental digital logic gate. Its behavior is the opposite of an AND gate. While an AND gate produces a high output only when all its inputs are high, a NAND gate produces a low output only when all its inputs are high.
Let's analyze the operation of a two-input NAND gate. It performs the logical operation of NOT(A AND B), which can be represented by the Boolean expression $\overline{A \cdot B}$. The output is the inverse of the result of the AND operation on the inputs A and B.
NAND Gate Truth Table Analysis
The truth table summarizes the output of a logic gate for all possible combinations of inputs. For a two-input NAND gate with inputs A and B and output Q, the truth table is as follows:
| Input A | Input B | AND Output (A $\cdot$ B) | NAND Output ($\overline{A \cdot B}$) |
|---|---|---|---|
| 0 | 0 | 0 | 1 |
| 0 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 0 |
From the truth table, we can clearly see the output (NAND Output) for each combination of inputs A and B.
- When inputs are 0, 0: The AND output is 0, and the NAND output is the inverse of 0, which is 1.
- When inputs are 0, 1: The AND output is 0, and the NAND output is the inverse of 0, which is 1.
- When inputs are 1, 0: The AND output is 0, and the NAND output is the inverse of 0, which is 1.
- When inputs are 1, 1: The AND output is 1, and the NAND output is the inverse of 1, which is 0.
The question asks for the input combination when the NAND gate output will be low. Looking at the truth table, the NAND output is '0' (low) only in the last row, where both Input A and Input B are '1'.
Therefore, the NAND gate output is low if and only if both inputs are 1.
Revision Table: Key Digital Logic Concepts
| Concept | Description | Symbol |
|---|---|---|
| Logic Gate | An elementary building block of a digital circuit that performs a basic logical function. | Various shapes (e.g., triangle for NOT, 'D' shape for AND). |
| Truth Table | A table showing all possible input combinations to a logic gate or circuit and their corresponding outputs. | Tabular format. |
| Boolean Algebra | A mathematical system for analyzing and simplifying digital circuits. Uses variables that can only have two values, 0 (low) and 1 (high). | Symbols like $\cdot$ (AND), + (OR), $\overline{\text{A}}$ (NOT). |
| High/Low States | Represent the two binary states in digital logic, typically corresponding to voltage levels (e.g., high voltage for 1, low voltage for 0). | Represented by 1 and 0. |
Additional Information on NAND Gate Properties
The NAND gate is considered a "universal gate". This means that any other logic gate (AND, OR, NOT, XOR, XNOR) can be constructed using only NAND gates. This property makes NAND gates very important in digital circuit design and integrated circuits.
Understanding the NAND gate's behavior, particularly when its output is low or high, is crucial for analyzing and designing digital systems. Remember that 'low' typically corresponds to a logic 0, and 'high' corresponds to a logic 1 in positive logic systems.
Important Questions from Basic Gates
Which of the following gates gives output 1 when any one of the input is 1?
Minimum number of NAND gates required to implement the following binary equation $Y = (A+B)(\overline{C \cdot D})$
Which of the following statements are true?
(i) Every logic network is equivalent to one using just NAND gates or just NOR gates.
(ii) Boolean expressions and logic networks correspond to labelled acyclic digraphs.
(iii) No two Boolean algebras with n atoms are isomorphic.
(iv) Non-zero elements of finite Boolean algebras are not uniquely expressible as joins of atoms.In a PLA, what components are used to implement the combinational logic functions?
Which of the following logic gates has output low when one of the inputs is high?
