**Convert the following circuit to a Boolean equation (do not simplify):**The diagram illustrates a digital logic circuit composed of several logic gates. The circuit consists of three inputs labeled `a`, `b`, and `c`, and one output labeled `F`.1. **AND, OR, and NOT Gates:** - The input `a` is connected to a NOT gate, generating the output `¬a` (NOT a). - Inputs `a` and `b` are fed into a three-input AND gate. The third input is `¬c`, which comes from a NOT gate connected to `c`. - The output of this AND gate is one of the inputs to the final OR gate.2. **Intermediate Processing:** - Inputs `a`, `b`, and `c` are combined in a second AND gate. - This AND gate’s output is fed into the same OR gate previously mentioned.3. **Final Processing:** - Both outputs from the two AND gates are fed into an OR gate. The output of this OR gate is the final output `F`.**Boolean Equation:**The Boolean equation for the circuit can be written as:\[ F = (¬a \cdot b \cdot ¬c) + (a \cdot b \cdot c) \]This equation represents the output `F` as a sum (OR) of the products (ANDs) of the inverted and non-inverted inputs.

Answered: Convert the following circuit to a…

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

Section: Chapter Questions

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**Convert the following circuit to a Boolean equation (do not simplify):**

The diagram illustrates a digital logic circuit composed of several logic gates. The circuit consists of three inputs labeled `a`, `b`, and `c`, and one output labeled `F`.

1. **AND, OR, and NOT Gates:**

- The input `a` is connected to a NOT gate, generating the output `¬a` (NOT a).
- Inputs `a` and `b` are fed into a three-input AND gate. The third input is `¬c`, which comes from a NOT gate connected to `c`.
- The output of this AND gate is one of the inputs to the final OR gate.

2. **Intermediate Processing:**

- Inputs `a`, `b`, and `c` are combined in a second AND gate.
- This AND gate’s output is fed into the same OR gate previously mentioned.

3. **Final Processing:**

- Both outputs from the two AND gates are fed into an OR gate. The output of this OR gate is the final output `F`.

**Boolean Equation:**

The Boolean equation for the circuit can be written as:

\[ F = (¬a \cdot b \cdot ¬c) + (a \cdot b \cdot c) \]

This equation represents the output `F` as a sum (OR) of the products (ANDs) of the inverted and non-inverted inputs.

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The AND gate is an electronic circuit that gives a high output (1) only if all its inputs are high. A dot (.) is used to show the AND operation i.e. A.B.

The OR gate is an electronic circuit that gives a high output (1) if one or more of its inputs are high. A plus (+) is used to show the OR operation.

The NOT gate is an electronic circuit that produces an inverted version of the input at its output. This is shown as A', or A with a bar over the top.

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