Which gate is represented by the following truth table? Input A Input B Output 0 0 0 0 1 0 1 0 0 1 1 1
AND
Understanding the Given Truth Table
The question asks us to identify the logic gate represented by the provided truth table. A truth table is a table that shows all possible input combinations to a logic gate or digital circuit and the corresponding output.
| Input A | Input B | Output |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Analyzing the Truth Table to Identify the Logic Gate
Let's carefully look at the output column based on the different input combinations from the truth table:
- When Input A is 0 and Input B is 0, the Output is 0.
- When Input A is 0 and Input B is 1, the Output is 0.
- When Input A is 1 and Input B is 0, the Output is 0.
- When Input A is 1 and Input B is 1, the Output is 1.
We can see that the output is 1 (High) only when both inputs, A and B, are 1 (High). In all other cases where at least one input is 0 (Low), the output is 0 (Low). This specific behavior is characteristic of an AND gate.
Comparing with Other Common Logic Gates
To be sure, let's consider the behavior of other common logic gates:
- OR Gate: An OR gate outputs 1 if *any* of its inputs are 1. Its truth table would have outputs 0, 1, 1, 1 for inputs (0,0), (0,1), (1,0), (1,1) respectively. This does not match the given truth table.
- NAND Gate: A NAND gate (NOT-AND) outputs 0 only if *all* inputs are 1. It's the opposite of an AND gate. Its truth table would have outputs 1, 1, 1, 0. This does not match.
- NOR Gate: A NOR gate (NOT-OR) outputs 1 only if *all* inputs are 0. Its truth table would have outputs 1, 0, 0, 0. This does not match.
The provided truth table uniquely matches the operation of an AND gate.
Conclusion: The Represented Logic Gate
Based on our analysis of the truth table, where the output is high (1) only when both inputs are high (1), the logic gate represented is the AND gate.
Revision Table: Key Logic Gate Truth Tables (2 Inputs)
Understanding the standard truth tables helps in identifying logic gates quickly.
| Input A | Input B | AND | OR | NAND | NOR | XOR | XNOR |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 |
| 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 |
| 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 |
| 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 |
Additional Information on Logic Gates and Truth Tables
Logic gates are the basic digital electronic circuits that perform logical operations. Each logic gate follows a Boolean function and has a corresponding truth table that defines its behavior for all possible input combinations.
The AND gate is a fundamental gate. Its Boolean expression for two inputs A and B is written as $Y = A \cdot B$ or simply $Y = AB$. This signifies that the output Y is true (1) only when both A AND B are true (1).
Truth tables are essential tools in digital electronics for:
- Defining the function of a logic gate or circuit.
- Analyzing the output of a circuit for given inputs.
- Simplifying Boolean expressions and logic circuits.
By learning the truth tables of basic gates like AND, OR, NOT, NAND, NOR, XOR, and XNOR, you can understand how digital systems process information.
Important Questions from Logic Gates
A two-input logic gate is giving high output only when both the inputs are high. For all other input conditions, the output is low. Select the correct logic gate.
The output is high only if one of the input is high. The above statement represents _____
The number of gate inputs, required to realize expression ABC + AB̅CD + EF̅ + AD is
Which of the following is logically equivalent?
A. ¬p → (q → r) and q → (p ∨ r)
B. (p → q) → r and p → (q → r)
C. (p → q) → (r → s) and (p → r) → (q → s)
Choose the correct answer from the options given below :
Consider the expression Y = P ⨁ Q ⨁ R where P, Q, R are the input variables and Y is the output variable. Y will be logic 0 if
(A) an odd number of input variables are 1
(B) an even number of input variables are 1
(C) an odd number of inputs variables are 0
(D) an even number of input variable are 0
(E) an odd number of input variable between 0 and 1
Choose the correct answer from the options given below:
