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1) Given the gate diagram shown, create the equivalent Boolean equation.

1) Given the gate diagram shown, create the equivalent Boolean equation.

EBK ELECTRICAL WIRING RESIDENTIAL
EBK ELECTRICAL WIRING RESIDENTIAL
19th Edition
ISBN:9781337516549
Author:Simmons
Publisher:Simmons
Chapter26: Smoke, Heat, Carbon Monoxide Alarms, And Security Systems
Section: Chapter Questions
Problem 13R: Carbon monoxide is ____________, and is ____________, ____________, and ____________.
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1) Given the gate diagram shown, create the equivalent Boolean equation.

2) Create a truth table of the equation[Solution from #1]

3) Give Boolean equation in POS form from Truth Table in #2?

4) Give Boolean equation in SOP form from Truth Table in #2?

5) Simplify SOP form using Identities[Solution from #4]

6) Simplify SOP form using Identities[Solution from #4]

OR XOR XOR OR NOT N
Transcribed Image Text:OR XOR XOR OR NOT N
Boolean Identities Identity Name Identity Law Null (or Dominance) Law AND Form OR Form 1x = x 0+x= X Ox = 0 1+X = 1 Idempotent Law XX = X X+X = X Inverse Law XX = 0 X+X = 1 Commutative Law ху %3D ух X+y = y+X (ху)z %3D х(уz) x+yZ %3D (x+у)(х+2) x(у+2) %3D ху+Xz x(x+у) — х (xy) = X+ỹ Associative Law (X+y)+Z = X+(y+Z) Distributive Law = Absorption Law X+xy = X (X+y) = xỹ DeMorgan's Law Double Complement Law X= X
Transcribed Image Text:Boolean Identities Identity Name Identity Law Null (or Dominance) Law AND Form OR Form 1x = x 0+x= X Ox = 0 1+X = 1 Idempotent Law XX = X X+X = X Inverse Law XX = 0 X+X = 1 Commutative Law ху %3D ух X+y = y+X (ху)z %3D х(уz) x+yZ %3D (x+у)(х+2) x(у+2) %3D ху+Xz x(x+у) — х (xy) = X+ỹ Associative Law (X+y)+Z = X+(y+Z) Distributive Law = Absorption Law X+xy = X (X+y) = xỹ DeMorgan's Law Double Complement Law X= X
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