Deck 12: Boolean Algebra

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سؤال
The idempotent laws in a Boolean algebra state that and .
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لقلب البطاقة.
سؤال
In questions mark each statement TRUE or FALSE.
In questions mark each statement TRUE or FALSE.  <div style=padding-top: 35px>
سؤال
In questions mark each statement TRUE or FALSE.
In questions mark each statement TRUE or FALSE.  <div style=padding-top: 35px>
سؤال
In questions mark each statement TRUE or FALSE.
In questions mark each statement TRUE or FALSE.  <div style=padding-top: 35px>
سؤال
There are Boolean functions with 2 variables.
سؤال
There are Boolean functions with 3 variables.
سؤال
In questions mark each statement TRUE or FALSE.
In questions mark each statement TRUE or FALSE.  <div style=padding-top: 35px>
سؤال
Using Using   can be written in terms of  <div style=padding-top: 35px> can be written in terms of Using   can be written in terms of  <div style=padding-top: 35px>
سؤال
There are Boolean functions with 4 variables.
سؤال
In questions mark each statement TRUE or FALSE.
In questions mark each statement TRUE or FALSE.  <div style=padding-top: 35px>
سؤال
In questions mark each statement TRUE or FALSE.
In questions mark each statement TRUE or FALSE.  <div style=padding-top: 35px>
سؤال
In questions mark each statement TRUE or FALSE.
In questions mark each statement TRUE or FALSE.  <div style=padding-top: 35px>
سؤال
In questions mark each statement TRUE or FALSE.
In questions mark each statement TRUE or FALSE.  <div style=padding-top: 35px>
سؤال
When written as a product of maxterms (in the variables x and y ), When written as a product of maxterms (in the variables  x  and  y  ),  <div style=padding-top: 35px>
سؤال
Using PPP can be written in terms of PPP
سؤال
In questions mark each statement TRUE or FALSE.
In questions mark each statement TRUE or FALSE.  <div style=padding-top: 35px>
سؤال
In questions mark each statement TRUE or FALSE.
In questions mark each statement TRUE or FALSE.  <div style=padding-top: 35px>
سؤال
In questions mark each statement TRUE or FALSE.
In questions mark each statement TRUE or FALSE.  <div style=padding-top: 35px>
سؤال
When written as a sum of minterms (in the variables x and y ), When written as a sum of minterms (in the variables  x  and  y  ),  <div style=padding-top: 35px>
سؤال
In questions mark each statement TRUE or FALSE.
In questions mark each statement TRUE or FALSE.  <div style=padding-top: 35px>
سؤال
Find the sum-of-products expansion of the Boolean function f(x, y, z) that is 1 if and only if either x = z = 1
and y = 0, or x = 0 and y = z = 1.
سؤال
Find the sum-of-products expansion of the Boolean function Find the sum-of-products expansion of the Boolean function   that is 1 if and only if either   and  <div style=padding-top: 35px> that is 1 if and only if either Find the sum-of-products expansion of the Boolean function   that is 1 if and only if either   and  <div style=padding-top: 35px> and Find the sum-of-products expansion of the Boolean function   that is 1 if and only if either   and  <div style=padding-top: 35px>
سؤال
Write x(y + 1) as a sum-of-products in the variables x and y.
سؤال
If If   , find  <div style=padding-top: 35px> , find If   , find  <div style=padding-top: 35px>
سؤال
Find the sum-of-products expansion of the Boolean function f(x, y, z) that is 1 if and only if exactly two of
the three variables have value 1.
سؤال
(a) Find a Boolean function (a) Find a Boolean function   such that   and   otherwise. (b) Write     using only . and  <div style=padding-top: 35px> such that (a) Find a Boolean function   such that   and   otherwise. (b) Write     using only . and  <div style=padding-top: 35px> and (a) Find a Boolean function   such that   and   otherwise. (b) Write     using only . and  <div style=padding-top: 35px>
otherwise.
(b) Write (a) Find a Boolean function   such that   and   otherwise. (b) Write     using only . and  <div style=padding-top: 35px> using only . and (a) Find a Boolean function   such that   and   otherwise. (b) Write     using only . and  <div style=padding-top: 35px>
سؤال
Write Write   as a sum-of-products in the variables  <div style=padding-top: 35px> as a sum-of-products in the variables Write   as a sum-of-products in the variables  <div style=padding-top: 35px>
سؤال
Write Write   as a sum-of-products in the variables  x  and  y .<div style=padding-top: 35px> as a sum-of-products in the variables x and y .
سؤال
In questions mark each statement TRUE or FALSE.
In questions mark each statement TRUE or FALSE.  <div style=padding-top: 35px>
سؤال
If If    , find  <div style=padding-top: 35px> , find If    , find  <div style=padding-top: 35px>
سؤال
Write Write   as a sum-of-products in the variables  <div style=padding-top: 35px> as a sum-of-products in the variables Write   as a sum-of-products in the variables  <div style=padding-top: 35px>
سؤال
Find a Boolean function Find a Boolean function   such that   and  <div style=padding-top: 35px> such that Find a Boolean function   such that   and  <div style=padding-top: 35px> and Find a Boolean function   such that   and  <div style=padding-top: 35px>
سؤال
Write x + z as a sum-of-products in the variables x, y, and z.
سؤال
Write Write   as a sum-of-products in the variables  x  and  y .<div style=padding-top: 35px> as a sum-of-products in the variables x and y .
سؤال
Write 1 as a sum-of-products in the variables x and y.
سؤال
In questions mark each statement TRUE or FALSE.
In questions mark each statement TRUE or FALSE.  <div style=padding-top: 35px>
سؤال
If If   , find  <div style=padding-top: 35px> , find If   , find  <div style=padding-top: 35px>
سؤال
Write Write   as a sum-of-products in the variables  <div style=padding-top: 35px> as a sum-of-products in the variables Write   as a sum-of-products in the variables  <div style=padding-top: 35px>
سؤال
Write Write   as a sum-of-products in the variables  <div style=padding-top: 35px> as a sum-of-products in the variables Write   as a sum-of-products in the variables  <div style=padding-top: 35px>
سؤال
If If   , find  <div style=padding-top: 35px> , find If   , find  <div style=padding-top: 35px>
سؤال
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent
Boolean variables.
x(x + y) = x + y x.
سؤال
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent
Boolean variables.
x + x y + x = x.
سؤال
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent
Boolean variables.
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent Boolean variables.  <div style=padding-top: 35px>
سؤال
Using only the five properties associative laws, commutative laws, distributive laws, identity laws, and complement laws, prove that Using only the five properties associative laws, commutative laws, distributive laws, identity laws, and complement laws, prove that   is true in all Boolean algebras.<div style=padding-top: 35px> is true in all Boolean algebras.
سؤال
If If   find  <div style=padding-top: 35px> find If   find  <div style=padding-top: 35px>
سؤال
If If   find  <div style=padding-top: 35px> find If   find  <div style=padding-top: 35px>
سؤال
Show that the Boolean function F given by Show that the Boolean function  F  given by   simplifies to   by using only the definition of a Boolean algebra.<div style=padding-top: 35px> simplifies to Show that the Boolean function  F  given by   simplifies to   by using only the definition of a Boolean algebra.<div style=padding-top: 35px> by using only the definition of a Boolean algebra.
سؤال
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent
Boolean variables.
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent Boolean variables.  <div style=padding-top: 35px>
سؤال
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent
Boolean variables.
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent Boolean variables.  <div style=padding-top: 35px>
سؤال
Using only the five properties associative laws, commutative laws, distributive laws, identity laws, and com-
plement laws, prove that x x = x is true in all Boolean algebras.
سؤال
Show that the Boolean function F given by Show that the Boolean function  F  given by   simplifies to   by using only the difinition of a booleab algebra .<div style=padding-top: 35px> simplifies to Show that the Boolean function  F  given by   simplifies to   by using only the difinition of a booleab algebra .<div style=padding-top: 35px> by using only the difinition of a booleab algebra .
سؤال
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent
Boolean variables.
x + y + z = x y z.
سؤال
Prove that F=G , where Prove that  F=G , where   and  <div style=padding-top: 35px> and Prove that  F=G , where   and  <div style=padding-top: 35px>
سؤال
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent
Boolean variables.
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent Boolean variables.  <div style=padding-top: 35px>
سؤال
Using only the five properties associative laws, commutative laws, distributive laws, identity laws, and complement laws, prove that Using only the five properties associative laws, commutative laws, distributive laws, identity laws, and complement laws, prove that   is true in all Boolean algebras.<div style=padding-top: 35px> is true in all Boolean algebras.
سؤال
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent
Boolean variables.
x + x y z = x.
سؤال
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent
Boolean variables.
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent Boolean variables.  <div style=padding-top: 35px>
سؤال
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent
Boolean variables.
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent Boolean variables.  <div style=padding-top: 35px>
سؤال
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent
Boolean variables.
(x x + 1) = (x + 1)(x + 1).
سؤال
Using only the five properties associative laws, commutative laws, distributive laws, identity laws, and complement laws, prove that x x = x is true in all boolean algebras .
سؤال
Give a reason for each step in the proof that x + x = x is true in Boolean algebras. Your reasons should
come from the following: associative laws for addition and multiplication, commutative laws for addition
and multiplication, distributive law for multiplication over addition and distributive law for addition over
multiplication, identity laws, unit property, and zero property. Give a reason for each step in the proof that x + x = x is true in Boolean algebras. Your reasons should come from the following: associative laws for addition and multiplication, commutative laws for addition and multiplication, distributive law for multiplication over addition and distributive law for addition over multiplication, identity laws, unit property, and zero property.  <div style=padding-top: 35px>
سؤال
Let Let   . Draw a logic gate diagram for  F .<div style=padding-top: 35px> . Draw a logic gate diagram for F .
سؤال
Use a Karnaugh map to minimize the sum-of-products expression Use a Karnaugh map to minimize the sum-of-products expression  <div style=padding-top: 35px>
سؤال
Use the Quine-McCluskey method to simplify the Boolean expression Use the Quine-McCluskey method to simplify the Boolean expression  <div style=padding-top: 35px>
سؤال
A circuit is to be built that takes the numbers 0 through 9 as inputs (1 = 0001, 2 = 0010, . . . , 9 = 1001). Let A circuit is to be built that takes the numbers 0 through 9 as inputs (1 = 0001, 2 = 0010, . . . , 9 = 1001). Let   be the Boolean function that produces an output of 1 if and only if the input is an odd number. Find a Karnaugh map for G and use the map and don't care conditions to find a simple expression for G.<div style=padding-top: 35px> be the Boolean function that produces an output of 1 if and only if the input is an odd number.
Find a Karnaugh map for G and use the map and don't care conditions to find a simple expression for
G.
سؤال
Procomplemenve that thetation,setandof realthenurealmbners,umwithbers 0additionand 1 aands them0ultiplicationand the 1 respof realectivnelyum, bisersnotasa+Boandolean· , negationalgebra. as
سؤال
Draw a logic gate diagram for the Boolean function Draw a logic gate diagram for the Boolean function  <div style=padding-top: 35px>
سؤال
Let https://d2lvgg3v3hfg70.cloudfront.net/TB34225555/Let https://d2lvgg3v3hfg70.cloudfront.net/TB34225555/ . Show that  F  can be simplified to give  <div style=padding-top: 35px> . Show that F can be simplified to give Let https://d2lvgg3v3hfg70.cloudfront.net/TB34225555/ . Show that  F  can be simplified to give  <div style=padding-top: 35px>
سؤال
Give a reason for each step in the proof that Give a reason for each step in the proof that   is true in Boolean algebras. Your reasons should come from the following: associative laws for addition and multiplication, commutative laws for addition and multiplication, distributive law for multiplication over addition and distributive law for addition over multiplication, identity laws, unit property, and zero property.  <div style=padding-top: 35px> is true in Boolean algebras. Your reasons should
come from the following: associative laws for addition and multiplication, commutative laws for addition
and multiplication, distributive law for multiplication over addition and distributive law for addition over
multiplication, identity laws, unit property, and zero property. Give a reason for each step in the proof that   is true in Boolean algebras. Your reasons should come from the following: associative laws for addition and multiplication, commutative laws for addition and multiplication, distributive law for multiplication over addition and distributive law for addition over multiplication, identity laws, unit property, and zero property.  <div style=padding-top: 35px>
سؤال
Give a reason for each step in the proof that x + xy = x is true in Boolean algebras. Your reasons should
come from the following: associative laws for addition and multiplication, commutative laws for addition
and multiplication, distributive law for multiplication over addition and distributive law for addition over
multiplication, identity laws, unit property, zero property, and idempotent laws. Give a reason for each step in the proof that x + xy = x is true in Boolean algebras. Your reasons should come from the following: associative laws for addition and multiplication, commutative laws for addition and multiplication, distributive law for multiplication over addition and distributive law for addition over multiplication, identity laws, unit property, zero property, and idempotent laws.  <div style=padding-top: 35px>
سؤال
Use the Quine-McCluskey method to simplify the Boolean expression x y z + x y z + x y z + x y z + x y z
سؤال
A circuit is to be built that takes the numbers 0 through 9 as inputs (1 = 0001, 2 = 0010, . . . , 9 = 1001). Let A circuit is to be built that takes the numbers 0 through 9 as inputs (1 = 0001, 2 = 0010, . . . , 9 = 1001). Let   be the Boolean function that produces an output of 1 if and only if the input is an even number. Find a Karnaugh map for F and use the map and don't care conditions to find a simple expression for F.<div style=padding-top: 35px> be the Boolean function that produces an output of 1 if and only if the input is an even number.
Find a Karnaugh map for F and use the map and don't care conditions to find a simple expression for
F.
سؤال
Let F(x, y, z) = y (x z) + y x + y z. Use a Karnaugh map to simplify the function F .
سؤال
Use a Karnaugh map to minimize the sum-of-products expression Use a Karnaugh map to minimize the sum-of-products expression  <div style=padding-top: 35px>
سؤال
Let Let   Draw a logic gate diagram for  F .<div style=padding-top: 35px> Draw a logic gate diagram for F .
سؤال
Construct a circuit using inverters, OR gates, and AND gates that gives an output of 1 if and only if three
people on a committee do not all vote the same.
سؤال
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent
Boolean variables.
(0 + x)(1 + x) = x x.
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ملء الشاشة (f)
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Deck 12: Boolean Algebra
1
The idempotent laws in a Boolean algebra state that and .
x + x = x, x · x = x.
2
In questions mark each statement TRUE or FALSE.
In questions mark each statement TRUE or FALSE.
True
3
In questions mark each statement TRUE or FALSE.
In questions mark each statement TRUE or FALSE.
True
4
In questions mark each statement TRUE or FALSE.
In questions mark each statement TRUE or FALSE.
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5
There are Boolean functions with 2 variables.
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6
There are Boolean functions with 3 variables.
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7
In questions mark each statement TRUE or FALSE.
In questions mark each statement TRUE or FALSE.
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8
Using Using   can be written in terms of  can be written in terms of Using   can be written in terms of
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9
There are Boolean functions with 4 variables.
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10
In questions mark each statement TRUE or FALSE.
In questions mark each statement TRUE or FALSE.
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11
In questions mark each statement TRUE or FALSE.
In questions mark each statement TRUE or FALSE.
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12
In questions mark each statement TRUE or FALSE.
In questions mark each statement TRUE or FALSE.
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13
In questions mark each statement TRUE or FALSE.
In questions mark each statement TRUE or FALSE.
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14
When written as a product of maxterms (in the variables x and y ), When written as a product of maxterms (in the variables  x  and  y  ),
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15
Using PPP can be written in terms of PPP
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16
In questions mark each statement TRUE or FALSE.
In questions mark each statement TRUE or FALSE.
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17
In questions mark each statement TRUE or FALSE.
In questions mark each statement TRUE or FALSE.
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18
In questions mark each statement TRUE or FALSE.
In questions mark each statement TRUE or FALSE.
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19
When written as a sum of minterms (in the variables x and y ), When written as a sum of minterms (in the variables  x  and  y  ),
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20
In questions mark each statement TRUE or FALSE.
In questions mark each statement TRUE or FALSE.
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افتح القفل للوصول البطاقات البالغ عددها 77 في هذه المجموعة.
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21
Find the sum-of-products expansion of the Boolean function f(x, y, z) that is 1 if and only if either x = z = 1
and y = 0, or x = 0 and y = z = 1.
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22
Find the sum-of-products expansion of the Boolean function Find the sum-of-products expansion of the Boolean function   that is 1 if and only if either   and  that is 1 if and only if either Find the sum-of-products expansion of the Boolean function   that is 1 if and only if either   and  and Find the sum-of-products expansion of the Boolean function   that is 1 if and only if either   and
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23
Write x(y + 1) as a sum-of-products in the variables x and y.
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24
If If   , find  , find If   , find
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25
Find the sum-of-products expansion of the Boolean function f(x, y, z) that is 1 if and only if exactly two of
the three variables have value 1.
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26
(a) Find a Boolean function (a) Find a Boolean function   such that   and   otherwise. (b) Write     using only . and  such that (a) Find a Boolean function   such that   and   otherwise. (b) Write     using only . and  and (a) Find a Boolean function   such that   and   otherwise. (b) Write     using only . and
otherwise.
(b) Write (a) Find a Boolean function   such that   and   otherwise. (b) Write     using only . and  using only . and (a) Find a Boolean function   such that   and   otherwise. (b) Write     using only . and
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27
Write Write   as a sum-of-products in the variables  as a sum-of-products in the variables Write   as a sum-of-products in the variables
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28
Write Write   as a sum-of-products in the variables  x  and  y . as a sum-of-products in the variables x and y .
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29
In questions mark each statement TRUE or FALSE.
In questions mark each statement TRUE or FALSE.
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30
If If    , find  , find If    , find
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31
Write Write   as a sum-of-products in the variables  as a sum-of-products in the variables Write   as a sum-of-products in the variables
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32
Find a Boolean function Find a Boolean function   such that   and  such that Find a Boolean function   such that   and  and Find a Boolean function   such that   and
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33
Write x + z as a sum-of-products in the variables x, y, and z.
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34
Write Write   as a sum-of-products in the variables  x  and  y . as a sum-of-products in the variables x and y .
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35
Write 1 as a sum-of-products in the variables x and y.
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36
In questions mark each statement TRUE or FALSE.
In questions mark each statement TRUE or FALSE.
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37
If If   , find  , find If   , find
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38
Write Write   as a sum-of-products in the variables  as a sum-of-products in the variables Write   as a sum-of-products in the variables
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39
Write Write   as a sum-of-products in the variables  as a sum-of-products in the variables Write   as a sum-of-products in the variables
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40
If If   , find  , find If   , find
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41
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent
Boolean variables.
x(x + y) = x + y x.
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42
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent
Boolean variables.
x + x y + x = x.
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43
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent
Boolean variables.
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent Boolean variables.
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44
Using only the five properties associative laws, commutative laws, distributive laws, identity laws, and complement laws, prove that Using only the five properties associative laws, commutative laws, distributive laws, identity laws, and complement laws, prove that   is true in all Boolean algebras. is true in all Boolean algebras.
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45
If If   find  find If   find
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46
If If   find  find If   find
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47
Show that the Boolean function F given by Show that the Boolean function  F  given by   simplifies to   by using only the definition of a Boolean algebra. simplifies to Show that the Boolean function  F  given by   simplifies to   by using only the definition of a Boolean algebra. by using only the definition of a Boolean algebra.
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48
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent
Boolean variables.
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent Boolean variables.
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49
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent
Boolean variables.
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent Boolean variables.
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50
Using only the five properties associative laws, commutative laws, distributive laws, identity laws, and com-
plement laws, prove that x x = x is true in all Boolean algebras.
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51
Show that the Boolean function F given by Show that the Boolean function  F  given by   simplifies to   by using only the difinition of a booleab algebra . simplifies to Show that the Boolean function  F  given by   simplifies to   by using only the difinition of a booleab algebra . by using only the difinition of a booleab algebra .
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52
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent
Boolean variables.
x + y + z = x y z.
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53
Prove that F=G , where Prove that  F=G , where   and  and Prove that  F=G , where   and
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54
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent
Boolean variables.
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent Boolean variables.
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55
Using only the five properties associative laws, commutative laws, distributive laws, identity laws, and complement laws, prove that Using only the five properties associative laws, commutative laws, distributive laws, identity laws, and complement laws, prove that   is true in all Boolean algebras. is true in all Boolean algebras.
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56
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent
Boolean variables.
x + x y z = x.
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57
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent
Boolean variables.
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent Boolean variables.
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58
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent
Boolean variables.
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent Boolean variables.
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59
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent
Boolean variables.
(x x + 1) = (x + 1)(x + 1).
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60
Using only the five properties associative laws, commutative laws, distributive laws, identity laws, and complement laws, prove that x x = x is true in all boolean algebras .
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61
Give a reason for each step in the proof that x + x = x is true in Boolean algebras. Your reasons should
come from the following: associative laws for addition and multiplication, commutative laws for addition
and multiplication, distributive law for multiplication over addition and distributive law for addition over
multiplication, identity laws, unit property, and zero property. Give a reason for each step in the proof that x + x = x is true in Boolean algebras. Your reasons should come from the following: associative laws for addition and multiplication, commutative laws for addition and multiplication, distributive law for multiplication over addition and distributive law for addition over multiplication, identity laws, unit property, and zero property.
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62
Let Let   . Draw a logic gate diagram for  F . . Draw a logic gate diagram for F .
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63
Use a Karnaugh map to minimize the sum-of-products expression Use a Karnaugh map to minimize the sum-of-products expression
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64
Use the Quine-McCluskey method to simplify the Boolean expression Use the Quine-McCluskey method to simplify the Boolean expression
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65
A circuit is to be built that takes the numbers 0 through 9 as inputs (1 = 0001, 2 = 0010, . . . , 9 = 1001). Let A circuit is to be built that takes the numbers 0 through 9 as inputs (1 = 0001, 2 = 0010, . . . , 9 = 1001). Let   be the Boolean function that produces an output of 1 if and only if the input is an odd number. Find a Karnaugh map for G and use the map and don't care conditions to find a simple expression for G. be the Boolean function that produces an output of 1 if and only if the input is an odd number.
Find a Karnaugh map for G and use the map and don't care conditions to find a simple expression for
G.
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66
Procomplemenve that thetation,setandof realthenurealmbners,umwithbers 0additionand 1 aands them0ultiplicationand the 1 respof realectivnelyum, bisersnotasa+Boandolean· , negationalgebra. as
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67
Draw a logic gate diagram for the Boolean function Draw a logic gate diagram for the Boolean function
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68
Let https://d2lvgg3v3hfg70.cloudfront.net/TB34225555/Let https://d2lvgg3v3hfg70.cloudfront.net/TB34225555/ . Show that  F  can be simplified to give  . Show that F can be simplified to give Let https://d2lvgg3v3hfg70.cloudfront.net/TB34225555/ . Show that  F  can be simplified to give
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69
Give a reason for each step in the proof that Give a reason for each step in the proof that   is true in Boolean algebras. Your reasons should come from the following: associative laws for addition and multiplication, commutative laws for addition and multiplication, distributive law for multiplication over addition and distributive law for addition over multiplication, identity laws, unit property, and zero property.  is true in Boolean algebras. Your reasons should
come from the following: associative laws for addition and multiplication, commutative laws for addition
and multiplication, distributive law for multiplication over addition and distributive law for addition over
multiplication, identity laws, unit property, and zero property. Give a reason for each step in the proof that   is true in Boolean algebras. Your reasons should come from the following: associative laws for addition and multiplication, commutative laws for addition and multiplication, distributive law for multiplication over addition and distributive law for addition over multiplication, identity laws, unit property, and zero property.
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70
Give a reason for each step in the proof that x + xy = x is true in Boolean algebras. Your reasons should
come from the following: associative laws for addition and multiplication, commutative laws for addition
and multiplication, distributive law for multiplication over addition and distributive law for addition over
multiplication, identity laws, unit property, zero property, and idempotent laws. Give a reason for each step in the proof that x + xy = x is true in Boolean algebras. Your reasons should come from the following: associative laws for addition and multiplication, commutative laws for addition and multiplication, distributive law for multiplication over addition and distributive law for addition over multiplication, identity laws, unit property, zero property, and idempotent laws.
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71
Use the Quine-McCluskey method to simplify the Boolean expression x y z + x y z + x y z + x y z + x y z
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72
A circuit is to be built that takes the numbers 0 through 9 as inputs (1 = 0001, 2 = 0010, . . . , 9 = 1001). Let A circuit is to be built that takes the numbers 0 through 9 as inputs (1 = 0001, 2 = 0010, . . . , 9 = 1001). Let   be the Boolean function that produces an output of 1 if and only if the input is an even number. Find a Karnaugh map for F and use the map and don't care conditions to find a simple expression for F. be the Boolean function that produces an output of 1 if and only if the input is an even number.
Find a Karnaugh map for F and use the map and don't care conditions to find a simple expression for
F.
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73
Let F(x, y, z) = y (x z) + y x + y z. Use a Karnaugh map to simplify the function F .
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74
Use a Karnaugh map to minimize the sum-of-products expression Use a Karnaugh map to minimize the sum-of-products expression
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75
Let Let   Draw a logic gate diagram for  F . Draw a logic gate diagram for F .
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76
Construct a circuit using inverters, OR gates, and AND gates that gives an output of 1 if and only if three
people on a committee do not all vote the same.
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77
In questions determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent
Boolean variables.
(0 + x)(1 + x) = x x.
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