A + B = Y is the Boolean function for
OR gate
Boolean Function Identification: A + B = Y
The question asks to identify which logic gate is represented by the Boolean function A + B = Y. This involves understanding the basic operations of digital logic gates and their corresponding Boolean expressions.
Understanding Boolean Algebra Symbols
In the context of Boolean algebra and digital logic, the '+' symbol is universally used to represent the logical OR operation. The OR operation results in a true output (logic 1) if one or more of its inputs are true (logic 1).
The OR Gate Explained
The OR gate is a digital circuit that performs the logical OR function. For an OR gate with inputs A and B, the output Y is true if input A is true, or input B is true, or both inputs are true. The mathematical representation of this operation in Boolean algebra is:
$A + B = Y$
The behavior of an OR gate can be clearly shown using a truth table:
| Input A | Input B | Output Y (A + B) |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
Other Logic Gates and Their Functions
To differentiate, let's review the standard Boolean expressions for the other options:
- AND Gate: Implemented by the Boolean expression
$A \cdot B = Y$. The output is true only if both inputs A and B are true. - NAND Gate: This is a Not-AND gate, represented by
$\neg (A \cdot B) = Y$. The output is false only if both inputs are true. - NOR Gate: This is a Not-OR gate, represented by
$\neg (A + B) = Y$. The output is true only if both inputs are false.
Conclusion
Comparing the given function A + B = Y with the standard representations, it is evident that this expression precisely defines the operation of an OR gate.
Important Questions from Basic Gates
Which of the following gates gives output 1 when any one of the input is 1?
The NAND gate output will be low if the two inputs are-
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?
