Q4. Consider number A of X bits stored in sign magnitude as shown in the figure below (most significant bit is the sign, X-1 bits magnitude). X could be any number starting from 2 and up. Design the digital circuit that can inform us (by making F=1) that if the number stored in this location was to be multiplied by 2, it would result in a number that could still be stored in the X-1 bits (i.e., no overflow would result). For example: · if X is 4, and the number is 0100 (+4 in decimal), the result is +8 and we cannot store +8 with X-1=3 bits. Therefore, F=0. · if X is 5, and the number is 1010 (-2 in decimal), the result is -4 and we can store -4 with X-1=4 bits. Therefore, F=1. You can assume that in your design you may use "wires" connected directly to the bit locations. Use the MINIMUM number of gates. Show all your work. X-1 bits Sign in Fequals to 1 if A*2 can still be stored in the X-1 bits ?
Q4. Consider number A of X bits stored in sign magnitude as shown in the figure below (most significant bit is the sign, X-1 bits magnitude). X could be any number starting from 2 and up. Design the digital circuit that can inform us (by making F=1) that if the number stored in this location was to be multiplied by 2, it would result in a number that could still be stored in the X-1 bits (i.e., no overflow would result). For example: · if X is 4, and the number is 0100 (+4 in decimal), the result is +8 and we cannot store +8 with X-1=3 bits. Therefore, F=0. · if X is 5, and the number is 1010 (-2 in decimal), the result is -4 and we can store -4 with X-1=4 bits. Therefore, F=1. You can assume that in your design you may use "wires" connected directly to the bit locations. Use the MINIMUM number of gates. Show all your work. X-1 bits Sign in Fequals to 1 if A*2 can still be stored in the X-1 bits ?
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Transcribed Image Text:Q4. Consider number A of X bits stored in sign magnitude as shown in the figure below (most significant bit is
the sign, X-1 bits magnitude). X could be any number starting from 2 and up. Design the digital circuit that can
inform us (by making F=1) that if the number stored in this location was to be multiplied by 2, it would result in
a number that could still be stored in the X-1 bits (i.e., no overflow would result). For example:
· if X is 4, and the number is 0100 (+4 in decimal), the result is +8 and we cannot store +8 with X-1=3 bits.
Therefore, F=0.
· if X is 5, and the number is 1010 (-2 in decimal), the result is -4 and we can store -4 with X-1=4 bits.
Therefore, F=1.
You can assume that in your design you may use "wires" connected directly to the bit locations. Use the
MINIMUM number of gates. Show all your work.
X-1 bits
Sign
in
Fequals to 1 if A*2 can still be
stored in the X-1 bits
?
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