Homework Answers
a)
(x+y.x)'
=x'.(y.x)' (demorgan's law)
=x'(y'+x') (demorgan's law)
=x'.y'+x'.x'(distributive law A.(B+C)=A.B+A.C)
=x'.y'+x' (Idempotent law A.A=A)
=x'+x'.y' (Commutative law)
=x' (absorption law A+AB=A where A=x', B=y')
b)
x.(z+y)+(x'+y)'
=x.z+x.y+(x'+y)' (distributive law)
=x.z+x.y+(x')'.(y') (demorgan's law)
=x.z+x.y+x.y' (double negation law (A')'=A)
=x.z+x.(y+y') (distributive law)
=x.z+x.1 (complement law A+A'=1)
=x.z+x
=x+xz
=x (absorption law)
c)
(x.y)'+x'.z+y'.z
=x'+y'+x'z+y'.z (demorgans law)
=x'+y'+z.(x'+y') (distributive law)
=x'+y'+(x'+y').z (commutative law)
=x'+y' (absorption law A+AB=A where A=x'+y' B=z)
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12. Prove the following properties of Boolean algebras. Give a reason for each step. a. (x...
prove properties of Boolean algebr just A B and C please! 4. Prove the following properties...
prove properties of Boolean algebr
just A B and C please!
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Draw the nonabbreviated logic diagram for Boolean expression (a'+b')((b'+c)+b'c) and prove it equals to b'+a'c. Give...
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7. (a) Find an example of a Boolean algebra with elements x, y, and z for which xty-x + z but yz. (b) Prove that in any Boolean algebra, if xy- z and+ yxz, then y -z 7. (a) Find an example of a...
7. (a) Find an example of a Boolean algebra with elements x, y, and z for which xty-x + z but yz. (b) Prove that in any Boolean algebra, if xy- z and+ yxz, then y -z
7. (a) Find an example of a Boolean algebra with elements x, y, and z for which xty-x + z but yz. (b) Prove that in any Boolean algebra, if xy- z and+ yxz, then y -z
[8] Using properties of Boolean algebra, simplify the following Boolean expressions so they could be built...
[8] Using properties of Boolean algebra, simplify the following Boolean expressions so they could be built with the minimum number of gates. a. X= A + BC + AB + ABC + B b. Y = AB + B(AC + BC + ABC' + A) C. W = ABC' + AB'C' + B'CD + A'C + BC d. Z = (A + B')' + (ABC')' +A(B + A'C)'
Use Boolean algebra to prove that wz, + wX + y'z + x'y (w' + x'...
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Simplify the following boolean expressions. Step by step please I would like to really understand it....
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prove properties of Boolean algebr
just A B and C please!
4. Prove the following properties of Boolean algebras. Give a reason for each step. * (b) x + (x-y) = x x . (x + y) x (absorption properties) (c) (x y -x'x y)' -xy(DeMorgan's Laws) x +(y (xz))(x + y) (x (modular properties) (e) (x+y)·(x, + y) = y y+ y-y y)+x)-x+y (x-y) .(y+x') = x . y g x+y'-x+ y +x y)' (h) ((x . y) ....
Prove with Boolean algebra that (x - y) + (x'-y)-y. Give a reason for each step in your proof.
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7. (a) Find an example of a Boolean algebra with elements x, y, and z for which xty-x + z but yz. (b) Prove that in any Boolean algebra, if xy- z and+ yxz, then y -z
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