Boolean expression and truth table 16 row pls

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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Unsimplified Boolean expression and truth table 16 row pls
This image depicts a logic circuit diagram composed of two OR gates and one AND gate. Here’s a detailed explanation of the elements and connections:

- **Inputs:**
  - A, B, C, D: These are the inputs to the logic gates.

- **Logic Gates:**
  - **OR Gate 1:** Takes inputs A and B. The output of this gate is connected to one of the inputs of the AND gate.
  - **OR Gate 2:** Takes inputs C and D. The output of this gate is connected to the other input of the AND gate.

- **AND Gate:**
  - Combines the outputs from the two OR gates. The final output of this AND gate is labeled as Y.

This setup can be used to calculate the logic output Y based on the binary inputs A, B, C, and D. The expression for Y can be represented as:
\[ Y = (A \lor B) \land (C \lor D) \]

This means Y is true if the combination of input conditions satisfies the expression above.
Transcribed Image Text:This image depicts a logic circuit diagram composed of two OR gates and one AND gate. Here’s a detailed explanation of the elements and connections: - **Inputs:** - A, B, C, D: These are the inputs to the logic gates. - **Logic Gates:** - **OR Gate 1:** Takes inputs A and B. The output of this gate is connected to one of the inputs of the AND gate. - **OR Gate 2:** Takes inputs C and D. The output of this gate is connected to the other input of the AND gate. - **AND Gate:** - Combines the outputs from the two OR gates. The final output of this AND gate is labeled as Y. This setup can be used to calculate the logic output Y based on the binary inputs A, B, C, and D. The expression for Y can be represented as: \[ Y = (A \lor B) \land (C \lor D) \] This means Y is true if the combination of input conditions satisfies the expression above.
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Step 1

Solution- The truth table and boolean expression is shown below-

The logic circuit shown in given figure has four inputs A, B, C and DForming a logic circuit with a combination of OR and AND gates.

Gate-1: ( OR gate)

 Two inputs A and B are given in logic gate - 1 .

The inputs A and B are connected to OR gate producing an output of A+B.

Let assume output of A+B =E

Gate-2: ( OR gate)

 Two inputs C and D are given in logic gate - 2 .

The inputs A and B are connected to OR gate producing an output of C+D.

Let assume output of C+D=F

 

Gate-3: (AND gate)

The logic gate-3 has two inputs. One input is obtained from the output of gate-1 and the second input is from logic gate -2.

The inputs A+B and C+D are connected to AND gate producing an output of (Y= A+B . C+D) or( Y=E.F)

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