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Yi D D Sum, Carryi+1

Yi D D Sum, Carryi+1

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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This diagram illustrates a digital logic circuit known as a Full Adder, which is used in computer arithmetic to add three binary bits: two significant bits \( x_i \) and \( y_i \), and a carry-in bit \( \text{Carry}_i \). ### Components: 1. **Inputs:** - \( x_i \) - \( y_i \) - \( \text{Carry}_i \) 2. **Outputs:** - \( \text{Sum}_i \) - \( \text{Carry}_{i+1} \) ### Logic Gates and Connections: - **XOR Gates:** - The first XOR gate takes inputs \( x_i \) and \( y_i \) and outputs an intermediate value. - The output of this XOR gate is then XORed with \( \text{Carry}_i \) using another XOR gate to produce the final sum output (\( \text{Sum}_i \)). - **AND Gates:** - One AND gate takes inputs \( x_i \) and \( y_i \). - Another AND gate takes the output of the first XOR gate and \( \text{Carry}_i \). - **OR Gate:** - The outputs of both AND gates are fed into an OR gate to produce the carry-out (\( \text{Carry}_{i+1} \)). ### Function: The Full Adder calculates the sum and carry-out bit when adding three single binary digits, incorporating the incoming carry. The circuit correctly handles the carry-in, improving the handling of binary addition in sequential circuits.
Transcribed Image Text:This diagram illustrates a digital logic circuit known as a Full Adder, which is used in computer arithmetic to add three binary bits: two significant bits \( x_i \) and \( y_i \), and a carry-in bit \( \text{Carry}_i \). ### Components: 1. **Inputs:** - \( x_i \) - \( y_i \) - \( \text{Carry}_i \) 2. **Outputs:** - \( \text{Sum}_i \) - \( \text{Carry}_{i+1} \) ### Logic Gates and Connections: - **XOR Gates:** - The first XOR gate takes inputs \( x_i \) and \( y_i \) and outputs an intermediate value. - The output of this XOR gate is then XORed with \( \text{Carry}_i \) using another XOR gate to produce the final sum output (\( \text{Sum}_i \)). - **AND Gates:** - One AND gate takes inputs \( x_i \) and \( y_i \). - Another AND gate takes the output of the first XOR gate and \( \text{Carry}_i \). - **OR Gate:** - The outputs of both AND gates are fed into an OR gate to produce the carry-out (\( \text{Carry}_{i+1} \)). ### Function: The Full Adder calculates the sum and carry-out bit when adding three single binary digits, incorporating the incoming carry. The circuit correctly handles the carry-in, improving the handling of binary addition in sequential circuits.
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