Which gate is represented by the following truth table?Input A Input B Output 0 0 0 0 1 1 1 0 1 1 1 1
OR
Identifying the Logic Gate from its Truth Table
A truth table shows the output of a logic gate for all possible combinations of its inputs. To identify the logic gate, we need to compare the given truth table with the standard truth tables for common logic gates like AND, OR, XOR, and NOT.
Analyzing the Given Truth Table
The given truth table has two inputs, A and B, and one output. Let's examine its entries:
| Input A | Input B | Output |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
Comparing with Standard Logic Gate Truth Tables
Let's recall the truth tables for the common two-input logic gates:
AND Gate: The output is 1 only if both inputs are 1.
| Input A | Input B | Output (A AND B) |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
OR Gate: The output is 1 if at least one input is 1.
| Input A | Input B | Output (A OR B) |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
XOR Gate: The output is 1 if the inputs are different.
| Input A | Input B | Output (A XOR B) |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
The NOT gate is a single-input gate, so its truth table is not applicable for comparison with this two-input table.
Matching the Truth Table
Comparing the given truth table with the standard ones:
- For inputs (0, 0), the output is 0. This matches AND, OR, and XOR.
- For inputs (0, 1), the output is 1. This matches OR and XOR, but not AND.
- For inputs (1, 0), the output is 1. This matches OR and XOR, but not AND.
- For inputs (1, 1), the output is 1. This matches OR, but not AND or XOR.
Only the OR gate's truth table matches the given truth table exactly for all input combinations.
Conclusion
Based on the comparison of the given truth table with the standard logic gate truth tables, the gate represented by the table is the OR gate.
Revision Table: Logic Gate Truth Tables
| Gate | Inputs | Output | Condition for Output = 1 |
|---|---|---|---|
| AND | A, B | A & B | Only if A=1 AND B=1 |
| OR | A, B | A + B | If A=1 OR B=1 (or both) |
| XOR | A, B | A ⊕ B | If A <> B (Inputs are different) |
| NOT | A | ¯A | If A=0 |
Additional Information: Understanding Logic Gates
Logic gates are fundamental building blocks of digital electronic circuits. They perform basic logical operations. Understanding their truth tables is crucial for analyzing and designing digital circuits.
- Each gate performs a specific Boolean function.
- The output is determined solely by the current inputs.
- Complex digital systems, like computers, are built by combining many logic gates.
- Boolean algebra provides a mathematical way to analyze and simplify circuits composed of logic gates.
Important Questions from Boolean Algebra
How many different Boolean functions of degree n are there?
Consider a Boolean function of ‘n’ variables. The order of an algorithm that determines whether the Boolean function produces a output 1 is:
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