For the following logic circuit, the truth table is:
For the following logic circuit, the truth table is:
\(\begin{matrix} A &B &Y \\ 0&0 &0 \\ 0&1 &1 \\ 1&0 &1 \\ 1&1 &1 \end{matrix}\)
\(\begin{matrix} A &B &Y \\ 0&0 &1 \\ 0&1 &0 \\ 1&0 &1 \\ 1&1 &0 \end{matrix}\)
\(\begin{matrix} A &B &Y \\ 0&0 &0 \\ 0&1 &0 \\ 1&0 &0 \\ 1&1 &1 \end{matrix}\)
\(\begin{matrix} A &B &Y \\ 0&0 &1 \\ 0&1 &1 \\ 1&0 &1 \\ 1&1 &0 \end{matrix}\)
The Correct Option is C
Approach Solution - 1
The given logic circuit requires us to determine its corresponding truth table by analyzing the behavior of logic gates in the circuit. From the options provided, we need to identify which truth table represents the function of the circuit.
The circuit's behavior can be represented as a logical expression and then evaluated for every combination of inputs \(A\) and \(B\).
For this particular set of options, the correct behavior of the circuit is captured by the truth table representing the logical AND operation:
| A | B | Y |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Explanation: The AND gate only outputs 1 when both inputs are 1. Hence, the output \(Y\) is 1 only when \(A=1\) and \(B=1\), matching the correct truth table. This option reflects the behavior of a 2-input AND gate.
Approach Solution -2
The correct option is (C): \(\begin{matrix} A &B &Y \\ 0&0 &0 \\ 0&1 &0 \\ 1&0 &0 \\ 1&1 &1 \end{matrix}\)
Y=\(\bar{\bar{A}.\bar{B}}=\bar{\bar{A}}+\bar{\bar{B}}\)
=(A+B) OR Gate
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Concepts Used:
Logic Gates
AND Gate
It is the gate, where a circuit performs an AND operation. It has n number of input where (n >= 2) and one output.
OR Gate
It is the gate, where a circuit performs an OR operation. It has n number of input where (n >= 2) and one output.
NOT Gate
An inverter is also called NOT Gate. It has one input and one output where the input is A and the output is Y.
NAND Gate
A NAND operation is also called a NOT-AND operation. It has n number of input where (n >= 2) and one output.
NOR Gate
A NOR operation is also called a NOT-OR operation. It has n number of input where (n >= 2) and one output.
XOR Gate
XOR or Ex-OR gate is a specific type of gate that can be used in the half adder, full adder, and subtractor.
XNOR Gate
XNOR gate is a specific type of gate, which can be used in the half adder, full adder, and subtractor. The exclusive-NOR gate is flattened as an EX-NOR gate or sometimes as an X-NOR gate. It has n number of input (n >= 2) and one output.