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Show how the function f(w1, W2, W3) = m(1, 2, 3, 5, 6) can be implemented using a 3-to-8 binary decoder and an OR gate.

Show how the function f(w1, W2, W3) = m(1, 2, 3, 5, 6) can be implemented using a 3-to-8 binary decoder and an OR gate.

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
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write the verilog code that represents the function in problem 4.2 using a case statement.

***Attention: the problem (4.2) is attached as an image.

**Binary Decoder and OR Gate Implementation** This instructional guide explains how the function \( f(w_1, w_2, w_3) = \sum m(1, 2, 3, 5, 6) \) can be implemented using a 3-to-8 binary decoder and an OR gate. **Function Breakdown:** - The expression \(\sum m(1, 2, 3, 5, 6)\) represents a sum of minterms for the specified indices. - In a 3-variable expression, each combination of inputs \( w_1, w_2, \) and \( w_3 \) corresponds to an output from the decoder. **Implementation Steps:** 1. **3-to-8 Decoder**: - This device takes a 3-bit input (such as \( w_1, w_2, \) and \( w_3 \)) and activates one of its 8 output lines based on the binary representation of the inputs. - Each output line corresponds to one minterm. 2. **Minterm Selection**: - Activate the specific outputs of the decoder corresponding to the minterm indices \( 1, 2, 3, 5, \) and \( 6 \). 3. **OR Gate Integration**: - Connect the activated output lines to an OR gate. - The OR gate combines these active lines to produce the final output of the function. **Visual Explanation:** - **Decoder Diagram**: - Inputs: \( w_1, w_2, w_3 \) - Outputs: Lines for minterms \( m_0, m_1, m_2, \ldots, m_7 \) - **OR Gate Configuration**: - Inputs: Connected from decoder outputs \( m_1, m_2, m_3, m_5, \) and \( m_6 \). - Single Output: Represents the function \( f(w_1, w_2, w_3) \). This setup efficiently computes the desired Boolean function using basic digital logic components.
Transcribed Image Text:**Binary Decoder and OR Gate Implementation** This instructional guide explains how the function \( f(w_1, w_2, w_3) = \sum m(1, 2, 3, 5, 6) \) can be implemented using a 3-to-8 binary decoder and an OR gate. **Function Breakdown:** - The expression \(\sum m(1, 2, 3, 5, 6)\) represents a sum of minterms for the specified indices. - In a 3-variable expression, each combination of inputs \( w_1, w_2, \) and \( w_3 \) corresponds to an output from the decoder. **Implementation Steps:** 1. **3-to-8 Decoder**: - This device takes a 3-bit input (such as \( w_1, w_2, \) and \( w_3 \)) and activates one of its 8 output lines based on the binary representation of the inputs. - Each output line corresponds to one minterm. 2. **Minterm Selection**: - Activate the specific outputs of the decoder corresponding to the minterm indices \( 1, 2, 3, 5, \) and \( 6 \). 3. **OR Gate Integration**: - Connect the activated output lines to an OR gate. - The OR gate combines these active lines to produce the final output of the function. **Visual Explanation:** - **Decoder Diagram**: - Inputs: \( w_1, w_2, w_3 \) - Outputs: Lines for minterms \( m_0, m_1, m_2, \ldots, m_7 \) - **OR Gate Configuration**: - Inputs: Connected from decoder outputs \( m_1, m_2, m_3, m_5, \) and \( m_6 \). - Single Output: Represents the function \( f(w_1, w_2, w_3) \). This setup efficiently computes the desired Boolean function using basic digital logic components.
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