Answered: create a circuit for Full Adder…

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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create a circuit for Full Adder S=A'B'C'in+A'BCin+AB'Cin+ABC'in

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Step 1: Full Adder circuit

A Full Adder circuit adds three binary inputs A, B, and Cin (carry-in) and produces two outputs, Sum (S) and Carry-out (Cout). The expression you provided, S = A'B'Cin + A'BCin + AB'Cin + ABC'in, represents the Sum (S) output of the Full Adder. To create a Full Adder circuit based on this expression, we can follow these steps:

Implementing the XOR gates for S:
- A'B'Cin is equivalent to A'B'Cin
- A'BCin is equivalent to A'BCin
- AB'Cin is equivalent to AB'Cin
- ABC'in is equivalent to ABC'in
Implementing the AND gates for Cin (carry-in):
- A'B'Cin requires an AND gate for A', B', and Cin.
- A'BCin requires an AND gate for A', B, and Cin.
- AB'Cin requires an AND gate for A, B', and Cin.
- ABC'in requires an AND gate for A, B, and Cin'.
Implementing the OR gate for S:
- Connect the outputs of the XOR gates (S1, S2, S3, S4) to a single OR gate. This gate generates the Sum (S) output.
Implementing the OR gate for Cout (carry-out):
- Connect the carry-out outputs of the AND gates (Cout1, Cout2, Cout3, Cout4) to a single OR gate. This gate generates the Carry-out (Cout) output.

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