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Problem 3; Build a combinational circuit for a base 4 to binary encoder AND a binary to base 4 decoder. Create truth tables, Boolean expression for each output, and logic diagram Encoder Decoder

Problem 3; Build a combinational circuit for a base 4 to binary encoder AND a binary to base 4 decoder. Create truth tables, Boolean expression for each output, and logic diagram Encoder Decoder

Database System Concepts
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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## Problem 3: ### Objective: Build a combinational circuit for a base 4 to binary encoder and a binary to base 4 decoder. Create truth tables, Boolean expression for each output, and logic diagram. ### Components: 1. **Encoder:** - Inputs: \( i_0, i_1, i_2, i_3 \) - Outputs: \( q_0, q_1 \) 2. **Decoder:** - Outputs/Inputs are illustrated, but not specifically labeled. ### Explanation: - **Encoder Diagram:** - A rectangle labeled "Encoder" has four lines leading into the left side labeled \( i_0, i_1, i_2, i_3 \) and two lines leading out from the right side labeled \( q_0, q_1 \). - **Decoder Diagram:** - A rectangle labeled "Decoder" with lines entering/exiting but without specific labels for these connections. ### Tasks: - **Truth Tables:** - Construct a table that represents the relationship between input combinations and their corresponding outputs for both the encoder and decoder. - **Boolean Expressions:** - Derive the Boolean expressions for the outputs \( q_0 \) and \( q_1 \) of the encoder. - **Logic Diagram:** - Illustrate the encoder and decoder functions using logic gates based on the developed truth tables and Boolean expressions. By creating these representations, you'll understand how the base 4 to binary encoding and binary to base 4 decoding work in digital circuits.
Transcribed Image Text:## Problem 3: ### Objective: Build a combinational circuit for a base 4 to binary encoder and a binary to base 4 decoder. Create truth tables, Boolean expression for each output, and logic diagram. ### Components: 1. **Encoder:** - Inputs: \( i_0, i_1, i_2, i_3 \) - Outputs: \( q_0, q_1 \) 2. **Decoder:** - Outputs/Inputs are illustrated, but not specifically labeled. ### Explanation: - **Encoder Diagram:** - A rectangle labeled "Encoder" has four lines leading into the left side labeled \( i_0, i_1, i_2, i_3 \) and two lines leading out from the right side labeled \( q_0, q_1 \). - **Decoder Diagram:** - A rectangle labeled "Decoder" with lines entering/exiting but without specific labels for these connections. ### Tasks: - **Truth Tables:** - Construct a table that represents the relationship between input combinations and their corresponding outputs for both the encoder and decoder. - **Boolean Expressions:** - Derive the Boolean expressions for the outputs \( q_0 \) and \( q_1 \) of the encoder. - **Logic Diagram:** - Illustrate the encoder and decoder functions using logic gates based on the developed truth tables and Boolean expressions. By creating these representations, you'll understand how the base 4 to binary encoding and binary to base 4 decoding work in digital circuits.
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