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6. A logic circuit consists of four gates as shown A В out В С What is the output? (A) 0 (B) A CB. C (C) A B C+A B (D) A.BA B+B. C 6. The Boolean expression for the circuit is A BB+C out Applying De Morgan's first theorem gives (А Ф В): (В+ C) out (А Ө В). (В+ С) The result of the EXCLUSIVE-OR is true when the inputs are different A BA B АӨВ = A BA B The negation of the EXCLUSIVE-OR is A B = A B+AB Applying De Morgan's first theorem gives (A B) (A B) (А + B) (A + В) A B - (A B) (AB) The distributive law gives AAA.B B. AB.B АФВ = 0 + A BB. A 0 = A. BA. B Substitute this result into the equation for the output and use the distributive law = (A B A B) (B C) = A B.B+ A B C+ A B. BA. B. C = 0 + A BC+ A B+ A B. C = A. B C+ A B+A B. C out Use the distributive law to factor A Bout of the second and third terms. = A B. C+ (A B) (1 C) out A BC+ A B.1 =A B. C+ A B The answer is (C).

6. A logic circuit consists of four gates as shown A В out В С What is the output? (A) 0 (B) A CB. C (C) A B C+A B (D) A.BA B+B. C 6. The Boolean expression for the circuit is A BB+C out Applying De Morgan's first theorem gives (А Ф В): (В+ C) out (А Ө В). (В+ С) The result of the EXCLUSIVE-OR is true when the inputs are different A BA B АӨВ = A BA B The negation of the EXCLUSIVE-OR is A B = A B+AB Applying De Morgan's first theorem gives (A B) (A B) (А + B) (A + В) A B - (A B) (AB) The distributive law gives AAA.B B. AB.B АФВ = 0 + A BB. A 0 = A. BA. B Substitute this result into the equation for the output and use the distributive law = (A B A B) (B C) = A B.B+ A B C+ A B. BA. B. C = 0 + A BC+ A B+ A B. C = A. B C+ A B+A B. C out Use the distributive law to factor A Bout of the second and third terms. = A B. C+ (A B) (1 C) out A BC+ A B.1 =A B. C+ A B The answer is (C).

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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6. A logic circuit consists of four gates as shown A В out В С What is the output? (A) 0 (B) A CB. C (C) A B C+A B (D) A.BA B+B. C 6. The Boolean expression for the circuit is A BB+C out Applying De Morgan's first theorem gives (А Ф В): (В+ C) out (А Ө В). (В+ С) The result of the EXCLUSIVE-OR is true when the inputs are different A BA B АӨВ = A BA B The negation of the EXCLUSIVE-OR is A B = A B+AB Applying De Morgan's first theorem gives (A B) (A B) (А + B) (A + В) A B - (A B) (AB) The distributive law gives AAA.B B. AB.B АФВ = 0 + A BB. A 0 = A. BA. B Substitute this result into the equation for the output and use the distributive law = (A B A B) (B C) = A B.B+ A B C+ A B. BA. B. C = 0 + A BC+ A B+ A B. C = A. B C+ A B+A B. C out Use the distributive law to factor A Bout of the second and third terms. = A B. C+ (A B) (1 C) out A BC+ A B.1 =A B. C+ A B The answer is (C).
Transcribed Image Text:6. A logic circuit consists of four gates as shown A В out В С What is the output? (A) 0 (B) A CB. C (C) A B C+A B (D) A.BA B+B. C 6. The Boolean expression for the circuit is A BB+C out Applying De Morgan's first theorem gives (А Ф В): (В+ C) out (А Ө В). (В+ С) The result of the EXCLUSIVE-OR is true when the inputs are different A BA B АӨВ = A BA B The negation of the EXCLUSIVE-OR is A B = A B+AB Applying De Morgan's first theorem gives (A B) (A B) (А + B) (A + В) A B - (A B) (AB) The distributive law gives AAA.B B. AB.B АФВ = 0 + A BB. A 0 = A. BA. B Substitute this result into the equation for the output and use the distributive law = (A B A B) (B C) = A B.B+ A B C+ A B. BA. B. C = 0 + A BC+ A B+ A B. C = A. B C+ A B+A B. C out Use the distributive law to factor A Bout of the second and third terms. = A B. C+ (A B) (1 C) out A BC+ A B.1 =A B. C+ A B The answer is (C).
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