## 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.

a base 4 to Binary Encoder : - The 4 to 2 encoder consist of 4 inputs Y0, Y1, Y2, & Y3 and 2…

Answered: Problem 3; Build a combinational…

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

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

## 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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