1. Use the 2-input version of the basic AND, OR, NOT gates to implement the following Boolean expression. Insert a drawing of your circuit here. Expression: \((A + B) \overline{C}\)Use the 2-input version of the basic AND, OR, NOT gates to implement the following Boolean expression. Insert a drawing of your circuit here. Expression: \(\overline{(AB)(\overline{BC})}\)Write the Boolean expression that is equivalent to the following circuit.**Diagram Explanation:**The diagram consists of the following components:- **Inputs:** Four inputs labeled A, B, C, and D. - **Gates:** - Two 2-input OR gates. The first OR gate takes inputs A and B; the second OR gate takes inputs C and D. - A 2-input AND gate. The outputs from the two OR gates are connected to the inputs of this AND gate. - A NOT gate (inverter). The output from the AND gate is connected to the input of the NOT gate. - **Output:** - The output of the NOT gate represents the final output of the circuit. To find the Boolean expression for this circuit, label the OR gate outputs as follows: \(X = A + B\) \(Y = C + D\)The output of the AND gate becomes: \(Z = XY = (A + B)(C + D)\)Finally, the NOT gate inverts the AND gate output: \(\overline{Z} = \overline{(A + B)(C + D)}\)The equivalent Boolean expression for the circuit is \(\overline{(A + B)(C + D)}\).

The 2-input OR gate gives the logical addition as output. The 2-input AND gate gives the logical…

1. Use the 2-input version of the basic AND, OR, NOT gates to implement the following Boolean expression. Insert a drawing of your circuit here. Expression: (A + B)T Use the 2-input version of the basic AND, OR, NOT gates to implement the following Boolean expression. Insert a drawing of your circuit here. Expression: (AB)(BC) Write the Boolean expression that is equivalent to the following circuit. A B. D

1. Use the 2-input version of the basic AND, OR, NOT gates to implement the following Boolean expression. Insert a drawing of your circuit here. Expression: (A + B)T Use the 2-input version of the basic AND, OR, NOT gates to implement the following Boolean expression. Insert a drawing of your circuit here. Expression: (AB)(BC) Write the Boolean expression that is equivalent to the following circuit. A B. D

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

Problem 1PE

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Question

1. Use the 2-input version of the basic AND, OR, NOT gates to implement the following Boolean expression. Insert a drawing of your circuit here. Expression: \((A + B) \overline{C}\)

Use the 2-input version of the basic AND, OR, NOT gates to implement the following Boolean expression. Insert a drawing of your circuit here. Expression: \(\overline{(AB)(\overline{BC})}\)

Write the Boolean expression that is equivalent to the following circuit.

**Diagram Explanation:**

The diagram consists of the following components:

- **Inputs:** Four inputs labeled A, B, C, and D.

- **Gates:**
- Two 2-input OR gates. The first OR gate takes inputs A and B; the second OR gate takes inputs C and D.
- A 2-input AND gate. The outputs from the two OR gates are connected to the inputs of this AND gate.
- A NOT gate (inverter). The output from the AND gate is connected to the input of the NOT gate.

- **Output:**
- The output of the NOT gate represents the final output of the circuit.

To find the Boolean expression for this circuit, label the OR gate outputs as follows:
\(X = A + B\)
\(Y = C + D\)

The output of the AND gate becomes:
\(Z = XY = (A + B)(C + D)\)

Finally, the NOT gate inverts the AND gate output:
\(\overline{Z} = \overline{(A + B)(C + D)}\)

The equivalent Boolean expression for the circuit is \(\overline{(A + B)(C + D)}\).

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