$1$s complement of $1011101$ is $\_\_\_\_\_\_\_\_\_\_\_\_$

a$.$

$1001101$

b$.$

$0101110$

c$.$

$0100010$

d$.$

$1100101$

Question $32$

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In Boolean algebra $0$ is a

a$.$

associative identity

b$.$

commutative property

c$.$

Additive identity

d$.$

identity element

Question $33$

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$($A $+$ B$)($A$*$ B$)=?$

a$.$

AB$$

b$.$

$1$

c$.$

$0$

d$.$

AB

Question $34$

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The commutative law of addition and multiplication indicates that:

a$.$

we can group variables in an AND or in an OR any way we want

b$.$

the way we OR or AND two variables is unimportant because the result is the same

c$.$

an expression can be expanded by multiplying term by term just the same as in ordinary algebra

d$.$

the factoring of Boolean expressions requires the multiplication of product terms that contain like variables

Question $35$

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The number of $0\text{'}$s in the output of POS expression $($A$\text{'}+$B$+$C$\text{'})($A$+$B$\text{'}+$C$)($A$\text{'}+$B$\text{'}+$C$)$ is$?$

a$.$

$3$

b$.$

$6$

c$.$

$4$

d$.$

$5$

Question $36$

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Given that F $=($A $+$ B$\text{'}+$ C$)($D $+$ E$),$ which of the following represents the only correct expression for F$\text{'}?$

a$.$

F$\text{'}=$ A'BC' $+$ D$\text{'}$E$\text{'}$

b$.$

F$\text{'}=($A$\text{'}+$ B $+$ C$\text{'})($D$\text{'}+$ E$\text{'})$

c$.$

F$\text{'}=$ AB'C $+$ DE

d$.$

F$\text{'}=$ A'BC'$+$ D$\text{'}+$ E$\text{'}$

Question $37$

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According to the Boolean algebra theorems x$.$x is equal to

a$.$

$1$

b$.$

x

c$.$

$0$

d$.$

x$\text{'}$

Question $38$

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The involution of A is equal to $\_\_\_\_\_\_\_\_\_$

a$.$

$1$

b$.$

A

c$.$

$0$

d$.$

A$$

Question $39$

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The expression Y$=$AB$+$BC$+$AC shows the $\_\_\_\_\_\_\_\_\_$ operation.

a$.$

SOP

b$.$

EX$-$OR

c$.$

POS

d$.$

NOR

Question $40$

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Simplify Y $=$ AB$+($A$+$ B$)$C$.$

a$.$

AB $+$ A

b$.$

AB$+$ C

c$.$

AB $+$ AC

d$.$

A$$B $+$ AC$$

Question $41$

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The equivalent of $($F$1)16$ in octal system is $\_\_\_\_\_\_\_\_\_$

a$.$

$362$

b$.$

$360$

c$.$

$362$

d$.$

$361$

Question $42$

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What is the primary motivation for using Boolean algebra to simplify logic expressions?

a$.$

It may make it easier to understand the overall function of the circuit.

b$.$

It may reduce the number of gates.

c$.$

It may reduce the number of inputs required.

d$.$

all of the above

Question $43$

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How many $0\text{'}$s are in the POS output for the SOP expression A$\text{'}+$ AB'C' $+$ ABC'

a$.$

$6$

b$.$

$2$

c$.$

$4$

d$.$

$5$

Question $44$

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Simplify $($A$.$B $+$ C$)($A$.$B $+$ D$)$ to the simpliest form.

a$.$

A$.$C $+$ D

b$.$

A$.$C $+$ B$.$D

c$.$

A$.$B $+$ C

d$.$

A$.$B $+$ C$.$D

Question $45$

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The advantage of $2$s complement system is that $\_\_\_\_\_\_\_\_\_$

a$.$

Only one arithmetic operation is required

b$.$

No arithmetic operations are required

c$.$

Two arithmetic operations are required

d$.$

Different Arithmetic operations are required