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Given the digital circuit below. a. What is the cost of this circuit? b. Convert the circuit to one with only NAND gates Xz X1 D D

Given the digital circuit below. a. What is the cost of this circuit? b. Convert the circuit to one with only NAND gates Xz X1 D D

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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### Digital Circuit Analysis **Task:** Given the digital circuit below: a. What is the cost of this circuit? b. Convert the circuit to one with only NAND gates. **Circuit Description:** The digital circuit involves three input variables: \( x_1 \), \( x_2 \), and \( x_3 \). The layout of the circuit is as follows: 1. **Inverters (NOT Gates):** - Two NOT gates are present, each receiving inputs from \( x_2 \) and \( x_3 \) respectively. 2. **AND Gates:** - Two AND gates are present. - The first AND gate takes two inputs: the output from the NOT gate connected to \( x_2 \) and the direct input from \( x_1 \). - The second AND gate takes two inputs: the output from the NOT gate connected to \( x_3 \) and the direct input from \( x_1 \). 3. **OR Gate:** - The outputs from the two AND gates are fed into an OR gate. - The final output of the circuit is labeled \( f \). **Diagram Explanation:** - The circuit is a combination of NOT, AND, and OR gates. - The function of the circuit can be analyzed by the Boolean expressions of the gates in sequence. - Note how the NOT gates are used to invert the variables \( x_2 \) and \( x_3 \) before they are input into the AND gates. - Understanding how these gates interact will help in converting the circuit to use only NAND gates, as required in part (b). This description facilitates the understanding of the logical structure and function of the circuit, enabling educational exploration of digital logic fundamentals.
Transcribed Image Text:### Digital Circuit Analysis **Task:** Given the digital circuit below: a. What is the cost of this circuit? b. Convert the circuit to one with only NAND gates. **Circuit Description:** The digital circuit involves three input variables: \( x_1 \), \( x_2 \), and \( x_3 \). The layout of the circuit is as follows: 1. **Inverters (NOT Gates):** - Two NOT gates are present, each receiving inputs from \( x_2 \) and \( x_3 \) respectively. 2. **AND Gates:** - Two AND gates are present. - The first AND gate takes two inputs: the output from the NOT gate connected to \( x_2 \) and the direct input from \( x_1 \). - The second AND gate takes two inputs: the output from the NOT gate connected to \( x_3 \) and the direct input from \( x_1 \). 3. **OR Gate:** - The outputs from the two AND gates are fed into an OR gate. - The final output of the circuit is labeled \( f \). **Diagram Explanation:** - The circuit is a combination of NOT, AND, and OR gates. - The function of the circuit can be analyzed by the Boolean expressions of the gates in sequence. - Note how the NOT gates are used to invert the variables \( x_2 \) and \( x_3 \) before they are input into the AND gates. - Understanding how these gates interact will help in converting the circuit to use only NAND gates, as required in part (b). This description facilitates the understanding of the logical structure and function of the circuit, enabling educational exploration of digital logic fundamentals.
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