You are asked to design a circuit to detect if an overflow occurs when subtracting two integers represented in two's complement: Z = X - Y. Let Sz, Sx, and Sy be the sign bit for Z, X, and Y respectively, and they are fed as input to the circuit. Let O be the output bit of the circuit, whose value is 1 if an overflow happens, and 0 if otherwise. a) Build the truth table for O as a Boolean function of Sx, Sy, and Sz. b) Write the canonical expression (sum-of-product) for the Boolean function defined in the part a. c) Implement the Boolean expression defined in part b with a circuit by using AND, OR, and NOT gates. Draw the wiring diagram.
You are asked to design a circuit to detect if an overflow occurs when subtracting two integers represented in two's complement: Z = X - Y. Let Sz, Sx, and Sy be the sign bit for Z, X, and Y respectively, and they are fed as input to the circuit. Let O be the output bit of the circuit, whose value is 1 if an overflow happens, and 0 if otherwise. a) Build the truth table for O as a Boolean function of Sx, Sy, and Sz. b) Write the canonical expression (sum-of-product) for the Boolean function defined in the part a. c) Implement the Boolean expression defined in part b with a circuit by using AND, OR, and NOT gates. Draw the wiring diagram.
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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![You are asked to design a circuit to detect if an overflow occurs when
subtracting two integers represented in two's complement: Z= X - Y. Let Sz, Sx,
and Sy be the sign bit for Z, X, and Y respectively, and they are fed as input to the
circuit. Let O be the output bit of the circuit, whose value is 1 if an overflow
happens, and 0 if otherwise.
a) Build the truth table for O as a Boolean function of Sx, Sy, and Sz.
b) Write the canonical expression (sum-of-product) for the Boolean function
defined in the part a.
c) Implement the Boolean expression defined in part b with a circuit by using
AND, OR, and NOT gates. Draw the wiring diagram.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F915aced1-4dd8-461c-8bbb-113909ad5fd4%2Fbc989d4a-e3a6-41b7-8af1-14442d292d04%2Foxoq8ko_processed.png&w=3840&q=75)
Transcribed Image Text:You are asked to design a circuit to detect if an overflow occurs when
subtracting two integers represented in two's complement: Z= X - Y. Let Sz, Sx,
and Sy be the sign bit for Z, X, and Y respectively, and they are fed as input to the
circuit. Let O be the output bit of the circuit, whose value is 1 if an overflow
happens, and 0 if otherwise.
a) Build the truth table for O as a Boolean function of Sx, Sy, and Sz.
b) Write the canonical expression (sum-of-product) for the Boolean function
defined in the part a.
c) Implement the Boolean expression defined in part b with a circuit by using
AND, OR, and NOT gates. Draw the wiring diagram.
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